t designs with small t, id ge 13300

• clan: 15-(32,16,12), 4 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(25,11,27360) (# 13299) : der= 5-(25,10,10944) and res= 5-(25,11,27360) - the given design is the residual.
• supplementary design of 6-(26,11,4560) (# 13444) with respect to smaller t
• residual design of supplementary of 6-(27,11,5985) (# 13446)
• derived from supplementary of 6-(27,12,15960) (# 13447)

# 13301: 5-(26,12,82080)

• clan: 15-(32,16,12), 4 times reduced t, 4 times derived, 2 times residual
• Tran van Trung construction (right) for 5-(25,11,27360) (# 13299) : der= 5-(25,11,27360) and res= 5-(25,12,54720) - the given design is the derived.
• supplementary design of 6-(26,12,11400) (# 13445) with respect to smaller t
• residual design of supplementary of 6-(27,12,15960) (# 13447)
• derived from supplementary of 6-(27,13,34200) (# 13448)
• derived from 6-(27,13,82080) (# 13459)

# 13302: 5-(27,11,52668)

• clan: 15-(32,16,12), 5 times reduced t, 5 times derived
• Tran van Trung construction (left) for 5-(26,11,38304) (# 13300) : der= 5-(26,10,14364) and res= 5-(26,11,38304) - the given design is the residual.
• supplementary design of 6-(27,11,5985) (# 13446) with respect to smaller t
• derived from supplementary of 6-(28,12,21945) (# 13449)

# 13303: 5-(27,12,120384)

• clan: 15-(32,16,12), 5 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(26,11,38304) (# 13300) : der= 5-(26,11,38304) and res= 5-(26,12,82080) - the given design is the derived.
• Tran van Trung construction (left) for 5-(26,12,82080) (# 13301) : der= 5-(26,11,38304) and res= 5-(26,12,82080) - the given design is the residual.
• supplementary design of 6-(27,12,15960) (# 13447) with respect to smaller t
• residual design of supplementary of 6-(28,12,21945) (# 13449)
• derived from supplementary of 6-(28,13,50160) (# 13450)

# 13304: 5-(27,13,225720)

• clan: 15-(32,16,12), 5 times reduced t, 3 times derived, 2 times residual
• Tran van Trung construction (right) for 5-(26,12,82080) (# 13301) : der= 5-(26,12,82080) and res= 5-(26,13,143640) - the given design is the derived.
• supplementary design of 6-(27,13,34200) (# 13448) with respect to smaller t
• residual design of supplementary of 6-(28,13,50160) (# 13450)
• derived from supplementary of 6-(28,14,94050) (# 13451)
• derived from 6-(28,14,225720) (# 13458)
• design 6-(27,13,82080) (# 13459) with respect to smaller t

# 13305: 5-(28,12,173052)

• clan: 15-(32,16,12), 6 times reduced t, 4 times derived
• Tran van Trung construction (right) for 5-(27,11,52668) (# 13302) : der= 5-(27,11,52668) and res= 5-(27,12,120384) - the given design is the derived.
• Tran van Trung construction (left) for 5-(27,12,120384) (# 13303) : der= 5-(27,11,52668) and res= 5-(27,12,120384) - the given design is the residual.
• supplementary design of 6-(28,12,21945) (# 13449) with respect to smaller t
• derived from supplementary of 6-(29,13,72105) (# 13453)

# 13306: 5-(28,13,346104)

• clan: 15-(32,16,12), 6 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(27,12,120384) (# 13303) : der= 5-(27,12,120384) and res= 5-(27,13,225720) - the given design is the derived.
• Tran van Trung construction (left) for 5-(27,13,225720) (# 13304) : der= 5-(27,12,120384) and res= 5-(27,13,225720) - the given design is the residual.
• supplementary design of 6-(28,13,50160) (# 13450) with respect to smaller t
• residual design of supplementary of 6-(29,13,72105) (# 13453)
• derived from supplementary of 6-(29,14,144210) (# 13454)
• derived from 6-(29,14,346104) (# 13472)

# 13307: 5-(28,14,576840)

• clan: 15-(32,16,12), 6 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 5-(27,13,225720) (# 13304)
• supplementary design of 6-(28,14,94050) (# 13451) with respect to smaller t
• residual design of supplementary of 6-(29,14,144210) (# 13454)
• Tran van Trung construction (left) for 5-(27,14,351120) (# 13456) : der= 5-(27,13,225720) and res= 5-(27,14,351120) - the given design is the residual.
• design 6-(28,14,225720) (# 13458) with respect to smaller t
• derived from supplementary of 6-(29,15,240350) (# 13470)
• residual design of 6-(29,14,346104) (# 13472)
• derived from 6-(29,15,576840) (# 13473)

# 13308: 5-(29,13,519156)

• clan: 15-(32,16,12), 7 times reduced t, 3 times derived
• Tran van Trung construction (right) for 5-(28,12,173052) (# 13305) : der= 5-(28,12,173052) and res= 5-(28,13,346104) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,13,346104) (# 13306) : der= 5-(28,12,173052) and res= 5-(28,13,346104) - the given design is the residual.
• supplementary design of 6-(29,13,72105) (# 13453) with respect to smaller t
• derived from supplementary of 6-(30,14,216315) (# 13461)

# 13309: 5-(29,14,922944)

• clan: 15-(32,16,12), 7 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(28,13,346104) (# 13306) : der= 5-(28,13,346104) and res= 5-(28,14,576840) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,14,576840) (# 13307) : der= 5-(28,13,346104) and res= 5-(28,14,576840) - the given design is the residual.
• supplementary design of 6-(29,14,144210) (# 13454) with respect to smaller t
• residual design of supplementary of 6-(30,14,216315) (# 13461)
• derived from supplementary of 6-(30,15,384560) (# 13462)
• derived from 6-(30,15,922944) (# 13471)
• design 6-(29,14,346104) (# 13472) with respect to smaller t

# 13310: 5-(30,14,1442100)

• clan: 15-(32,16,12), 8 times reduced t, 2 times derived
• Tran van Trung construction (right) for 5-(29,13,519156) (# 13308) : der= 5-(29,13,519156) and res= 5-(29,14,922944) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,14,922944) (# 13309) : der= 5-(29,13,519156) and res= 5-(29,14,922944) - the given design is the residual.
• supplementary design of 6-(30,14,216315) (# 13461) with respect to smaller t
• derived from supplementary of 6-(31,15,600875) (# 13467)
• derived from 6-(31,15,1442100) (# 13483)

# 13311: 5-(30,15,2307360)

• clan: 15-(32,16,12), 8 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(29,14,922944) (# 13309)
• supplementary design of 6-(30,15,384560) (# 13462) with respect to smaller t
• residual design of supplementary of 6-(31,15,600875) (# 13467)
• Tran van Trung construction (left) for 5-(29,15,1384416) (# 13469) : der= 5-(29,14,922944) and res= 5-(29,15,1384416) - the given design is the residual.
• design 6-(30,15,922944) (# 13471) with respect to smaller t
• derived from supplementary of 6-(31,16,961400) (# 13481)
• residual design of 6-(31,15,1442100) (# 13483)
• derived from 6-(31,16,2307360) (# 13484)

# 13312: 5-(31,15,3749460)

• clan: 15-(32,16,12), 9 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(30,14,1442100) (# 13310) : der= 5-(30,14,1442100) and res= 5-(30,15,2307360) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,15,2307360) (# 13311) : der= 5-(30,14,1442100) and res= 5-(30,15,2307360) - the given design is the residual.
• supplementary design of 6-(31,15,600875) (# 13467) with respect to smaller t
• derived from supplementary of 6-(32,16,1562275) (# 13474)
• derived from 6-(32,16,3749460) (# 13482)
• design 6-(31,15,1442100) (# 13483) with respect to smaller t

# 13313: 5-(32,16,9203220)

• clan: 15-(32,16,12), 10 times reduced t
• Tran van Trung construction with complementary design for 5-(31,15,3749460) (# 13312)
• supplementary design of 6-(32,16,1562275) (# 13474) with respect to smaller t
• Tran van Trung construction (left) for 5-(31,16,5453760) (# 13480) : der= 5-(31,15,3749460) and res= 5-(31,16,5453760) - the given design is the residual.
• design 6-(32,16,3749460) (# 13482) with respect to smaller t

# 13314: 7-(24,8,6)

• clan: 15-(32,16,6), 8 times derived
• PSL(2,23) (>= 132 isom. types) \cite{Bettenetal98b}

# 13315: 6-(23,7,6)

• clan: 15-(32,16,6), 9 times derived
• derived from 7-(24,8,6) (# 13314)

# 13316: 6-(23,8,48)

• clan: 15-(32,16,6), 8 times derived, 1 times residual
• residual design of 7-(24,8,6) (# 13314)
• derived from 7-(24,9,48) (# 13488)

# 13317: 6-(24,8,99)

• clan: 15-(32,16,11), 1 times reduced t, 8 times derived
• supplementary design of 7-(24,8,6) (# 13314) with respect to smaller t
• Tran van Trung construction (right) for 6-(23,7,11) (# 13318) : der= 6-(23,7,11) and res= 6-(23,8,88) - the given design is the derived.
• Tran van Trung construction (left) for 6-(23,8,88) (# 13319) : der= 6-(23,7,11) and res= 6-(23,8,88) - the given design is the residual.
• derived from supplementary of 7-(25,9,54) (# 13489)

# 13318: 6-(23,7,11)

• clan: 15-(32,16,11), 9 times derived
• derived from supplementary of 7-(24,8,6) (# 13314)

# 13319: 6-(23,8,88)

• clan: 15-(32,16,11), 8 times derived, 1 times residual
• residual design of supplementary of 7-(24,8,6) (# 13314)
• derived from supplementary of 7-(24,9,48) (# 13488)

# 13320: 5-(22,7,48)

• clan: 15-(32,16,6), 9 times derived, 1 times residual
• residual design of 6-(23,7,6) (# 13315)
• derived from 6-(23,8,48) (# 13316)
• residual design of supplementary of 6-(23,7,11) (# 13318)
• derived from supplementary of 6-(23,8,88) (# 13319)

# 13321: 5-(22,6,11)

• clan: 15-(32,16,11), 10 times derived
• derived from supplementary of 6-(23,7,6) (# 13315)
• derived from 6-(23,7,11) (# 13318)

# 13322: 5-(22,7,88)

• clan: 15-(32,16,11), 9 times derived, 1 times residual
• residual design of supplementary of 6-(23,7,6) (# 13315)
• derived from supplementary of 6-(23,8,48) (# 13316)
• residual design of 6-(23,7,11) (# 13318)
• derived from 6-(23,8,88) (# 13319)

# 13323: 6-(24,9,288)

• clan: 15-(32,16,6), 1 times reduced t, 7 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(23,8,48) (# 13316) : der= 6-(23,8,48) and res= 6-(23,9,240) - the given design is the derived.
• design 7-(24,9,48) (# 13488) with respect to smaller t
• residual design of 7-(25,9,54) (# 13489)
• derived from 7-(25,10,288) (# 13490)

# 13324: 6-(24,9,528)

• clan: 15-(32,16,11), 1 times reduced t, 7 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(23,8,88) (# 13319) : der= 6-(23,8,88) and res= 6-(23,9,440) - the given design is the derived.
• supplementary design of 7-(24,9,48) (# 13488) with respect to smaller t
• residual design of supplementary of 7-(25,9,54) (# 13489)
• derived from supplementary of 7-(25,10,288) (# 13490)

# 13325: 6-(25,9,342)

• clan: 15-(32,16,6), 2 times reduced t, 7 times derived
• Tran van Trung construction (left) for 6-(24,9,288) (# 13323) : der= 6-(24,8,54) and res= 6-(24,9,288) - the given design is the residual.
• design 7-(25,9,54) (# 13489) with respect to smaller t
• derived from 7-(26,10,342) (# 13491)

# 13326: 6-(25,10,1368)

• clan: 15-(32,16,6), 2 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(24,9,288) (# 13323) : der= 6-(24,9,288) and res= 6-(24,10,1080) - the given design is the derived.
• design 7-(25,10,288) (# 13490) with respect to smaller t
• residual design of 7-(26,10,342) (# 13491)
• derived from 7-(26,11,1368) (# 13492)

# 13327: 6-(25,9,627)

• clan: 15-(32,16,11), 2 times reduced t, 7 times derived
• Tran van Trung construction (left) for 6-(24,9,528) (# 13324) : der= 6-(24,8,99) and res= 6-(24,9,528) - the given design is the residual.
• supplementary design of 7-(25,9,54) (# 13489) with respect to smaller t
• derived from supplementary of 7-(26,10,342) (# 13491)

# 13328: 6-(25,10,2508)

• clan: 15-(32,16,11), 2 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(24,9,528) (# 13324) : der= 6-(24,9,528) and res= 6-(24,10,1980) - the given design is the derived.
• supplementary design of 7-(25,10,288) (# 13490) with respect to smaller t
• residual design of supplementary of 7-(26,10,342) (# 13491)
• derived from supplementary of 7-(26,11,1368) (# 13492)

# 13329: 6-(26,10,1710)

• clan: 15-(32,16,6), 3 times reduced t, 6 times derived
• Tran van Trung construction (right) for 6-(25,9,342) (# 13325) : der= 6-(25,9,342) and res= 6-(25,10,1368) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,10,1368) (# 13326) : der= 6-(25,9,342) and res= 6-(25,10,1368) - the given design is the residual.
• design 7-(26,10,342) (# 13491) with respect to smaller t
• derived from 7-(27,11,1710) (# 13493)

# 13330: 6-(26,11,5472)

• clan: 15-(32,16,6), 3 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(25,10,1368) (# 13326) : der= 6-(25,10,1368) and res= 6-(25,11,4104) - the given design is the derived.
• design 7-(26,11,1368) (# 13492) with respect to smaller t
• residual design of 7-(27,11,1710) (# 13493)
• derived from 7-(27,12,5472) (# 13494)

# 13331: 6-(26,10,3135)

• clan: 15-(32,16,11), 3 times reduced t, 6 times derived
• Tran van Trung construction (right) for 6-(25,9,627) (# 13327) : der= 6-(25,9,627) and res= 6-(25,10,2508) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,10,2508) (# 13328) : der= 6-(25,9,627) and res= 6-(25,10,2508) - the given design is the residual.
• supplementary design of 7-(26,10,342) (# 13491) with respect to smaller t
• derived from supplementary of 7-(27,11,1710) (# 13493)

# 13332: 6-(26,11,10032)

• clan: 15-(32,16,11), 3 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(25,10,2508) (# 13328) : der= 6-(25,10,2508) and res= 6-(25,11,7524) - the given design is the derived.
• supplementary design of 7-(26,11,1368) (# 13492) with respect to smaller t
• residual design of supplementary of 7-(27,11,1710) (# 13493)
• derived from supplementary of 7-(27,12,5472) (# 13494)

# 13333: 6-(27,12,19152)

• clan: 15-(32,16,6), 4 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(26,11,5472) (# 13330) : der= 6-(26,11,5472) and res= 6-(26,12,13680) - the given design is the derived.
• design 7-(27,12,5472) (# 13494) with respect to smaller t
• residual design of 7-(28,12,7182) (# 13495)
• derived from 7-(28,13,19152) (# 13496)

# 13334: 6-(27,11,13167)

• clan: 15-(32,16,11), 4 times reduced t, 5 times derived
• Tran van Trung construction (right) for 6-(26,10,3135) (# 13331) : der= 6-(26,10,3135) and res= 6-(26,11,10032) - the given design is the derived.
• Tran van Trung construction (left) for 6-(26,11,10032) (# 13332) : der= 6-(26,10,3135) and res= 6-(26,11,10032) - the given design is the residual.
• supplementary design of 7-(27,11,1710) (# 13493) with respect to smaller t
• derived from supplementary of 7-(28,12,7182) (# 13495)

# 13335: 6-(27,12,35112)

• clan: 15-(32,16,11), 4 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(26,11,10032) (# 13332) : der= 6-(26,11,10032) and res= 6-(26,12,25080) - the given design is the derived.
• supplementary design of 7-(27,12,5472) (# 13494) with respect to smaller t
• residual design of supplementary of 7-(28,12,7182) (# 13495)
• derived from supplementary of 7-(28,13,19152) (# 13496)

# 13336: 6-(28,12,26334)

• clan: 15-(32,16,6), 5 times reduced t, 4 times derived
• Tran van Trung construction (left) for 6-(27,12,19152) (# 13333) : der= 6-(27,11,7182) and res= 6-(27,12,19152) - the given design is the residual.
• design 7-(28,12,7182) (# 13495) with respect to smaller t
• derived from 7-(29,13,26334) (# 13497)

# 13337: 6-(28,13,60192)

• clan: 15-(32,16,6), 5 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(27,12,19152) (# 13333) : der= 6-(27,12,19152) and res= 6-(27,13,41040) - the given design is the derived.
• design 7-(28,13,19152) (# 13496) with respect to smaller t
• residual design of 7-(29,13,26334) (# 13497)
• derived from 7-(29,14,60192) (# 13498)

# 13338: 6-(28,12,48279)

• clan: 15-(32,16,11), 5 times reduced t, 4 times derived
• Tran van Trung construction (right) for 6-(27,11,13167) (# 13334) : der= 6-(27,11,13167) and res= 6-(27,12,35112) - the given design is the derived.
• Tran van Trung construction (left) for 6-(27,12,35112) (# 13335) : der= 6-(27,11,13167) and res= 6-(27,12,35112) - the given design is the residual.
• supplementary design of 7-(28,12,7182) (# 13495) with respect to smaller t
• derived from supplementary of 7-(29,13,26334) (# 13497)

# 13339: 6-(28,13,110352)

• clan: 15-(32,16,11), 5 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(27,12,35112) (# 13335) : der= 6-(27,12,35112) and res= 6-(27,13,75240) - the given design is the derived.
• supplementary design of 7-(28,13,19152) (# 13496) with respect to smaller t
• residual design of supplementary of 7-(29,13,26334) (# 13497)
• derived from supplementary of 7-(29,14,60192) (# 13498)

# 13340: 6-(29,13,86526)

• clan: 15-(32,16,6), 6 times reduced t, 3 times derived
• Tran van Trung construction (right) for 6-(28,12,26334) (# 13336) : der= 6-(28,12,26334) and res= 6-(28,13,60192) - the given design is the derived.
• Tran van Trung construction (left) for 6-(28,13,60192) (# 13337) : der= 6-(28,12,26334) and res= 6-(28,13,60192) - the given design is the residual.
• design 7-(29,13,26334) (# 13497) with respect to smaller t
• derived from 7-(30,14,86526) (# 13499)

# 13341: 6-(29,14,173052)

• clan: 15-(32,16,6), 6 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(28,13,60192) (# 13337) : der= 6-(28,13,60192) and res= 6-(28,14,112860) - the given design is the derived.
• derived from 7-(30,15,173052) (# 13346)
• derived from supplementary of 7-(30,15,317262) (# 13349)
• design 7-(29,14,60192) (# 13498) with respect to smaller t
• residual design of 7-(30,14,86526) (# 13499)

# 13342: 6-(29,13,158631)

• clan: 15-(32,16,11), 6 times reduced t, 3 times derived
• Tran van Trung construction (right) for 6-(28,12,48279) (# 13338) : der= 6-(28,12,48279) and res= 6-(28,13,110352) - the given design is the derived.
• Tran van Trung construction (left) for 6-(28,13,110352) (# 13339) : der= 6-(28,12,48279) and res= 6-(28,13,110352) - the given design is the residual.
• supplementary design of 7-(29,13,26334) (# 13497) with respect to smaller t
• derived from supplementary of 7-(30,14,86526) (# 13499)

# 13343: 6-(29,14,317262)

• clan: 15-(32,16,11), 6 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(28,13,110352) (# 13339) : der= 6-(28,13,110352) and res= 6-(28,14,206910) - the given design is the derived.
• derived from supplementary of 7-(30,15,173052) (# 13346)
• derived from 7-(30,15,317262) (# 13349)
• supplementary design of 7-(29,14,60192) (# 13498) with respect to smaller t
• residual design of supplementary of 7-(30,14,86526) (# 13499)

# 13344: 6-(30,14,259578)

• clan: 15-(32,16,6), 7 times reduced t, 2 times derived
• Tran van Trung construction (right) for 6-(29,13,86526) (# 13340) : der= 6-(29,13,86526) and res= 6-(29,14,173052) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,14,173052) (# 13341) : der= 6-(29,13,86526) and res= 6-(29,14,173052) - the given design is the residual.
• design 7-(30,14,86526) (# 13499) with respect to smaller t
• derived from 7-(31,15,259578) (# 13500)

# 13345: 6-(30,15,461472)

• clan: 15-(32,16,6), 7 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 6-(29,14,173052) (# 13341)
• design 7-(30,15,173052) (# 13346) with respect to smaller t
• supplementary design of 7-(30,15,317262) (# 13349) with respect to smaller t
• Tran van Trung construction (left) for 6-(29,15,288420) (# 13353) : der= 6-(29,14,173052) and res= 6-(29,15,288420) - the given design is the residual.
• residual design of 7-(31,15,259578) (# 13500)

# 13346: 7-(30,15,173052)

• clan: 15-(32,16,6), 6 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(29,14,173052) (# 13341)
• Tran van Trung construction with complementary design for 7-(29,14,60192) (# 13498)

# 13347: 6-(30,14,475893)

• clan: 15-(32,16,11), 7 times reduced t, 2 times derived
• Tran van Trung construction (right) for 6-(29,13,158631) (# 13342) : der= 6-(29,13,158631) and res= 6-(29,14,317262) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,14,317262) (# 13343) : der= 6-(29,13,158631) and res= 6-(29,14,317262) - the given design is the residual.
• supplementary design of 7-(30,14,86526) (# 13499) with respect to smaller t
• derived from supplementary of 7-(31,15,259578) (# 13500)

# 13348: 6-(30,15,846032)

• clan: 15-(32,16,11), 7 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 6-(29,14,317262) (# 13343)
• supplementary design of 7-(30,15,173052) (# 13346) with respect to smaller t
• design 7-(30,15,317262) (# 13349) with respect to smaller t
• Tran van Trung construction (left) for 6-(29,15,528770) (# 13354) : der= 6-(29,14,317262) and res= 6-(29,15,528770) - the given design is the residual.
• residual design of supplementary of 7-(31,15,259578) (# 13500)

# 13349: 7-(30,15,317262)

• clan: 15-(32,16,11), 6 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(29,14,317262) (# 13343)

# 13350: 6-(31,15,721050)

• clan: 15-(32,16,6), 8 times reduced t, 1 times derived
• Tran van Trung construction (right) for 6-(30,14,259578) (# 13344) : der= 6-(30,14,259578) and res= 6-(30,15,461472) - the given design is the derived.
• Tran van Trung construction (left) for 6-(30,15,461472) (# 13345) : der= 6-(30,14,259578) and res= 6-(30,15,461472) - the given design is the residual.
• derived from 7-(32,16,721050) (# 13357)
• derived from supplementary of 7-(32,16,1321925) (# 13361)
• design 7-(31,15,259578) (# 13500) with respect to smaller t

# 13351: 5-(29,15,692208)

• clan: 15-(32,16,6), 7 times reduced t, 1 times derived, 2 times residual
• residual design of 6-(30,15,461472) (# 13345)
• residual design of supplementary of 6-(30,15,846032) (# 13348)
• design 6-(29,15,288420) (# 13353) with respect to smaller t
• supplementary design of 6-(29,15,528770) (# 13354) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,15,403788) (# 13358) : der= 5-(28,14,288420) and res= 5-(28,15,403788) - the given design is the residual.

# 13352: 5-(29,15,1269048)

• clan: 15-(32,16,11), 7 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 6-(30,15,461472) (# 13345)
• residual design of 6-(30,15,846032) (# 13348)
• supplementary design of 6-(29,15,288420) (# 13353) with respect to smaller t
• design 6-(29,15,528770) (# 13354) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,15,740278) (# 13359) : der= 5-(28,14,528770) and res= 5-(28,15,740278) - the given design is the residual.

# 13353: 6-(29,15,288420)

• clan: 15-(32,16,6), 6 times reduced t, 1 times derived, 2 times residual
• residual design of 7-(30,15,173052) (# 13346)
• residual design of supplementary of 7-(30,15,317262) (# 13349)

# 13354: 6-(29,15,528770)

• clan: 15-(32,16,11), 6 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 7-(30,15,173052) (# 13346)
• residual design of 7-(30,15,317262) (# 13349)

# 13355: 6-(31,15,1321925)

• clan: 15-(32,16,11), 8 times reduced t, 1 times derived
• Tran van Trung construction (right) for 6-(30,14,475893) (# 13347) : der= 6-(30,14,475893) and res= 6-(30,15,846032) - the given design is the derived.
• Tran van Trung construction (left) for 6-(30,15,846032) (# 13348) : der= 6-(30,14,475893) and res= 6-(30,15,846032) - the given design is the residual.
• derived from supplementary of 7-(32,16,721050) (# 13357)
• derived from 7-(32,16,1321925) (# 13361)
• supplementary design of 7-(31,15,259578) (# 13500) with respect to smaller t

# 13356: 6-(32,16,1874730)

• clan: 15-(32,16,6), 9 times reduced t
• Tran van Trung construction with complementary design for 6-(31,15,721050) (# 13350)
• design 7-(32,16,721050) (# 13357) with respect to smaller t
• supplementary design of 7-(32,16,1321925) (# 13361) with respect to smaller t
• Tran van Trung construction (left) for 6-(31,16,1153680) (# 13364) : der= 6-(31,15,721050) and res= 6-(31,16,1153680) - the given design is the residual.

# 13357: 7-(32,16,721050)

• clan: 15-(32,16,6), 8 times reduced t
• Alltop construction for design 6-(31,15,721050) (# 13350)
• Tran van Trung construction with complementary design for 7-(31,15,259578) (# 13500)

# 13358: 5-(28,15,403788)

• clan: 15-(32,16,6), 6 times reduced t, 1 times derived, 3 times residual
• residual design of 6-(29,15,288420) (# 13353)
• residual design of supplementary of 6-(29,15,528770) (# 13354)

# 13359: 5-(28,15,740278)

• clan: 15-(32,16,11), 6 times reduced t, 1 times derived, 3 times residual
• residual design of supplementary of 6-(29,15,288420) (# 13353)
• residual design of 6-(29,15,528770) (# 13354)

# 13360: 6-(32,16,3437005)

• clan: 15-(32,16,11), 9 times reduced t
• Tran van Trung construction with complementary design for 6-(31,15,1321925) (# 13355)
• supplementary design of 7-(32,16,721050) (# 13357) with respect to smaller t
• design 7-(32,16,1321925) (# 13361) with respect to smaller t
• Tran van Trung construction (left) for 6-(31,16,2115080) (# 13365) : der= 6-(31,15,1321925) and res= 6-(31,16,2115080) - the given design is the residual.

# 13361: 7-(32,16,1321925)

• clan: 15-(32,16,11), 8 times reduced t
• Alltop construction for design 6-(31,15,1321925) (# 13355)

# 13362: 5-(31,16,2726880)

• clan: 15-(32,16,6), 9 times reduced t, 1 times residual
• residual design of 6-(32,16,1874730) (# 13356)
• residual design of supplementary of 6-(32,16,3437005) (# 13360)
• design 6-(31,16,1153680) (# 13364) with respect to smaller t
• supplementary design of 6-(31,16,2115080) (# 13365) with respect to smaller t
• Tran van Trung construction (left) for 5-(30,16,1573200) (# 13366) : der= 5-(30,15,1153680) and res= 5-(30,16,1573200) - the given design is the residual.

# 13363: 5-(31,16,4999280)

• clan: 15-(32,16,11), 9 times reduced t, 1 times residual
• residual design of supplementary of 6-(32,16,1874730) (# 13356)
• residual design of 6-(32,16,3437005) (# 13360)
• supplementary design of 6-(31,16,1153680) (# 13364) with respect to smaller t
• design 6-(31,16,2115080) (# 13365) with respect to smaller t
• Tran van Trung construction (left) for 5-(30,16,2884200) (# 13367) : der= 5-(30,15,2115080) and res= 5-(30,16,2884200) - the given design is the residual.

# 13364: 6-(31,16,1153680)

• clan: 15-(32,16,6), 8 times reduced t, 1 times residual
• residual design of 7-(32,16,721050) (# 13357)
• residual design of supplementary of 7-(32,16,1321925) (# 13361)

# 13365: 6-(31,16,2115080)

• clan: 15-(32,16,11), 8 times reduced t, 1 times residual
• residual design of supplementary of 7-(32,16,721050) (# 13357)
• residual design of 7-(32,16,1321925) (# 13361)

# 13366: 5-(30,16,1573200)

• clan: 15-(32,16,6), 8 times reduced t, 2 times residual
• residual design of 6-(31,16,1153680) (# 13364)
• residual design of supplementary of 6-(31,16,2115080) (# 13365)

# 13367: 5-(30,16,2884200)

• clan: 15-(32,16,11), 8 times reduced t, 2 times residual
• residual design of supplementary of 6-(31,16,1153680) (# 13364)
• residual design of 6-(31,16,2115080) (# 13365)

# 13368: 7-(24,8,7)

• clan: 15-(32,16,7), 8 times derived
• PSL(2,23) (>= 126 isom. types) \cite{Bettenetal98b}

# 13369: 6-(23,7,7)

• clan: 15-(32,16,7), 9 times derived
• derived from 7-(24,8,7) (# 13368)

# 13370: 6-(23,8,56)

• clan: 15-(32,16,7), 8 times derived, 1 times residual
• residual design of 7-(24,8,7) (# 13368)

# 13371: 6-(24,8,90)

• clan: 15-(32,16,10), 1 times reduced t, 8 times derived
• supplementary design of 7-(24,8,7) (# 13368) with respect to smaller t
• Tran van Trung construction (right) for 6-(23,7,10) (# 13372) : der= 6-(23,7,10) and res= 6-(23,8,80) - the given design is the derived.
• Tran van Trung construction (left) for 6-(23,8,80) (# 13373) : der= 6-(23,7,10) and res= 6-(23,8,80) - the given design is the residual.

# 13372: 6-(23,7,10)

• clan: 15-(32,16,10), 9 times derived
• derived from supplementary of 7-(24,8,7) (# 13368)

# 13373: 6-(23,8,80)

• clan: 15-(32,16,10), 8 times derived, 1 times residual
• residual design of supplementary of 7-(24,8,7) (# 13368)

# 13374: 5-(22,6,7)

• clan: 15-(32,16,7), 10 times derived
• derived from 6-(23,7,7) (# 13369)
• derived from supplementary of 6-(23,7,10) (# 13372)

# 13375: 5-(22,7,56)

• clan: 15-(32,16,7), 9 times derived, 1 times residual
• residual design of 6-(23,7,7) (# 13369)
• derived from 6-(23,8,56) (# 13370)
• residual design of supplementary of 6-(23,7,10) (# 13372)
• derived from supplementary of 6-(23,8,80) (# 13373)

# 13376: 5-(22,6,10)

• clan: 15-(32,16,10), 10 times derived
• derived from supplementary of 6-(23,7,7) (# 13369)
• derived from 6-(23,7,10) (# 13372)

# 13377: 5-(22,7,80)

• clan: 15-(32,16,10), 9 times derived, 1 times residual
• residual design of supplementary of 6-(23,7,7) (# 13369)
• derived from supplementary of 6-(23,8,56) (# 13370)
• residual design of 6-(23,7,10) (# 13372)
• derived from 6-(23,8,80) (# 13373)

# 13378: 5-(22,8,400)

• clan: 15-(32,16,10), 8 times derived, 2 times residual
• residual design of supplementary of 6-(23,8,56) (# 13370)
• residual design of 6-(23,8,80) (# 13373)

# 13379: 7-(24,8,8)

• clan: 15-(32,16,8), 8 times derived
• PSL(2,23) (>= 63 isom. types) PGL(2,23) (4 isom. types) no. of blocks = no. of 7-subsets \cite{Bettenetal98b}, \cite{Bettenetal97b}

# 13380: 6-(23,7,8)

• clan: 15-(32,16,8), 9 times derived
• derived from 7-(24,8,8) (# 13379)

# 13381: 6-(23,8,64)

• clan: 15-(32,16,8), 8 times derived, 1 times residual
• residual design of 7-(24,8,8) (# 13379)
• derived from 7-(24,9,64) (# 13501)

# 13382: 6-(24,8,81)

• clan: 15-(32,16,9), 1 times reduced t, 8 times derived
• supplementary design of 7-(24,8,8) (# 13379) with respect to smaller t
• Tran van Trung construction (right) for 6-(23,7,9) (# 13383) : der= 6-(23,7,9) and res= 6-(23,8,72) - the given design is the derived.
• Tran van Trung construction (left) for 6-(23,8,72) (# 13384) : der= 6-(23,7,9) and res= 6-(23,8,72) - the given design is the residual.
• derived from supplementary of 7-(25,9,72) (# 13502)

# 13383: 6-(23,7,9)

• clan: 15-(32,16,9), 9 times derived
• derived from supplementary of 7-(24,8,8) (# 13379)

# 13384: 6-(23,8,72)

• clan: 15-(32,16,9), 8 times derived, 1 times residual
• residual design of supplementary of 7-(24,8,8) (# 13379)
• derived from supplementary of 7-(24,9,64) (# 13501)

# 13385: 5-(22,6,8)

• clan: 15-(32,16,8), 10 times derived
• derived from 6-(23,7,8) (# 13380)
• derived from supplementary of 6-(23,7,9) (# 13383)

# 13386: 5-(22,7,64)

• clan: 15-(32,16,8), 9 times derived, 1 times residual
• residual design of 6-(23,7,8) (# 13380)
• derived from 6-(23,8,64) (# 13381)
• residual design of supplementary of 6-(23,7,9) (# 13383)
• derived from supplementary of 6-(23,8,72) (# 13384)

# 13387: 5-(22,6,9)

• clan: 15-(32,16,9), 10 times derived
• derived from supplementary of 6-(23,7,8) (# 13380)
• derived from 6-(23,7,9) (# 13383)

# 13388: 5-(22,7,72)

• clan: 15-(32,16,9), 9 times derived, 1 times residual
• residual design of supplementary of 6-(23,7,8) (# 13380)
• derived from supplementary of 6-(23,8,64) (# 13381)
• residual design of 6-(23,7,9) (# 13383)
• derived from 6-(23,8,72) (# 13384)

# 13389: 6-(24,9,384)

• clan: 15-(32,16,8), 1 times reduced t, 7 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(23,8,64) (# 13381) : der= 6-(23,8,64) and res= 6-(23,9,320) - the given design is the derived.
• design 7-(24,9,64) (# 13501) with respect to smaller t
• residual design of 7-(25,9,72) (# 13502)
• derived from 7-(25,10,384) (# 13503)

# 13390: 6-(24,9,432)

• clan: 15-(32,16,9), 1 times reduced t, 7 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(23,8,72) (# 13384) : der= 6-(23,8,72) and res= 6-(23,9,360) - the given design is the derived.
• supplementary design of 7-(24,9,64) (# 13501) with respect to smaller t
• residual design of supplementary of 7-(25,9,72) (# 13502)
• derived from supplementary of 7-(25,10,384) (# 13503)

# 13391: 6-(25,9,456)

• clan: 15-(32,16,8), 2 times reduced t, 7 times derived
• Tran van Trung construction (left) for 6-(24,9,384) (# 13389) : der= 6-(24,8,72) and res= 6-(24,9,384) - the given design is the residual.
• design 7-(25,9,72) (# 13502) with respect to smaller t
• derived from 7-(26,10,456) (# 13504)

# 13392: 6-(25,10,1824)

• clan: 15-(32,16,8), 2 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(24,9,384) (# 13389) : der= 6-(24,9,384) and res= 6-(24,10,1440) - the given design is the derived.
• design 7-(25,10,384) (# 13503) with respect to smaller t
• residual design of 7-(26,10,456) (# 13504)

# 13393: 6-(25,9,513)

• clan: 15-(32,16,9), 2 times reduced t, 7 times derived
• Tran van Trung construction (left) for 6-(24,9,432) (# 13390) : der= 6-(24,8,81) and res= 6-(24,9,432) - the given design is the residual.
• supplementary design of 7-(25,9,72) (# 13502) with respect to smaller t
• derived from supplementary of 7-(26,10,456) (# 13504)

# 13394: 6-(25,10,2052)

• clan: 15-(32,16,9), 2 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(24,9,432) (# 13390) : der= 6-(24,9,432) and res= 6-(24,10,1620) - the given design is the derived.
• supplementary design of 7-(25,10,384) (# 13503) with respect to smaller t
• residual design of supplementary of 7-(26,10,456) (# 13504)

# 13395: 6-(26,10,2280)

• clan: 15-(32,16,8), 3 times reduced t, 6 times derived
• Tran van Trung construction (right) for 6-(25,9,456) (# 13391) : der= 6-(25,9,456) and res= 6-(25,10,1824) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,10,1824) (# 13392) : der= 6-(25,9,456) and res= 6-(25,10,1824) - the given design is the residual.
• design 7-(26,10,456) (# 13504) with respect to smaller t
• derived from 7-(27,11,2280) (# 14307)

# 13396: 6-(26,11,7296)

• clan: 15-(32,16,8), 3 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(25,10,1824) (# 13392) : der= 6-(25,10,1824) and res= 6-(25,11,5472) - the given design is the derived.
• residual design of 7-(27,11,2280) (# 14307)

# 13397: 6-(26,10,2565)

• clan: 15-(32,16,9), 3 times reduced t, 6 times derived
• Tran van Trung construction (right) for 6-(25,9,513) (# 13393) : der= 6-(25,9,513) and res= 6-(25,10,2052) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,10,2052) (# 13394) : der= 6-(25,9,513) and res= 6-(25,10,2052) - the given design is the residual.
• supplementary design of 7-(26,10,456) (# 13504) with respect to smaller t
• derived from supplementary of 7-(27,11,2280) (# 14307)

# 13398: 6-(26,11,8208)

• clan: 15-(32,16,9), 3 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(25,10,2052) (# 13394) : der= 6-(25,10,2052) and res= 6-(25,11,6156) - the given design is the derived.
• residual design of supplementary of 7-(27,11,2280) (# 14307)

# 13399: 6-(27,12,25536)

• clan: 15-(32,16,8), 4 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(26,11,7296) (# 13396) : der= 6-(26,11,7296) and res= 6-(26,12,18240) - the given design is the derived.

created: Fri Oct 23 11:13:30 CEST 2009