t designs with small t, id ge 6500

• clan: 15-(32,16,6), 6 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(27,12,60192) (# 6498) : der= 5-(27,12,60192) and res= 5-(27,13,112860) - the given design is the derived.
• design 6-(28,13,60192) (# 13337) with respect to smaller t
• supplementary design of 6-(28,13,110352) (# 13339) with respect to smaller t
• residual design of 6-(29,13,86526) (# 13340)
• derived from 6-(29,14,173052) (# 13341)
• residual design of supplementary of 6-(29,13,158631) (# 13342)
• derived from supplementary of 6-(29,14,317262) (# 13343)

# 6501: 5-(29,13,259578)

• clan: 15-(32,16,6), 7 times reduced t, 3 times derived
• Tran van Trung construction (right) for 5-(28,12,86526) (# 6499) : der= 5-(28,12,86526) and res= 5-(28,13,173052) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,13,173052) (# 6500) : der= 5-(28,12,86526) and res= 5-(28,13,173052) - the given design is the residual.
• design 6-(29,13,86526) (# 13340) with respect to smaller t
• supplementary design of 6-(29,13,158631) (# 13342) with respect to smaller t
• derived from 6-(30,14,259578) (# 13344)
• derived from supplementary of 6-(30,14,475893) (# 13347)

# 6502: 5-(29,14,461472)

• clan: 15-(32,16,6), 7 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(28,13,173052) (# 6500) : der= 5-(28,13,173052) and res= 5-(28,14,288420) - the given design is the derived.
• design 6-(29,14,173052) (# 13341) with respect to smaller t
• supplementary design of 6-(29,14,317262) (# 13343) with respect to smaller t
• residual design of 6-(30,14,259578) (# 13344)
• derived from 6-(30,15,461472) (# 13345)
• residual design of supplementary of 6-(30,14,475893) (# 13347)
• derived from supplementary of 6-(30,15,846032) (# 13348)

# 6503: 5-(30,14,721050)

• clan: 15-(32,16,6), 8 times reduced t, 2 times derived
• Tran van Trung construction (right) for 5-(29,13,259578) (# 6501) : der= 5-(29,13,259578) and res= 5-(29,14,461472) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,14,461472) (# 6502) : der= 5-(29,13,259578) and res= 5-(29,14,461472) - the given design is the residual.
• design 6-(30,14,259578) (# 13344) with respect to smaller t
• supplementary design of 6-(30,14,475893) (# 13347) with respect to smaller t
• derived from 6-(31,15,721050) (# 13350)
• derived from supplementary of 6-(31,15,1321925) (# 13355)

# 6504: 5-(30,15,1153680)

• clan: 15-(32,16,6), 8 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(29,14,461472) (# 6502)
• design 6-(30,15,461472) (# 13345) with respect to smaller t
• supplementary design of 6-(30,15,846032) (# 13348) with respect to smaller t
• residual design of 6-(31,15,721050) (# 13350)
• Tran van Trung construction (left) for 5-(29,15,692208) (# 13351) : der= 5-(29,14,461472) and res= 5-(29,15,692208) - the given design is the residual.
• residual design of supplementary of 6-(31,15,1321925) (# 13355)
• derived from 6-(31,16,1153680) (# 13364)
• derived from supplementary of 6-(31,16,2115080) (# 13365)

# 6505: 5-(31,15,1874730)

• clan: 15-(32,16,6), 9 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(30,14,721050) (# 6503) : der= 5-(30,14,721050) and res= 5-(30,15,1153680) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,15,1153680) (# 6504) : der= 5-(30,14,721050) and res= 5-(30,15,1153680) - the given design is the residual.
• design 6-(31,15,721050) (# 13350) with respect to smaller t
• supplementary design of 6-(31,15,1321925) (# 13355) with respect to smaller t
• derived from 6-(32,16,1874730) (# 13356)
• derived from supplementary of 6-(32,16,3437005) (# 13360)

# 6506: 5-(32,16,4601610)

• clan: 15-(32,16,6), 10 times reduced t
• Tran van Trung construction with complementary design for 5-(31,15,1874730) (# 6505)
• design 6-(32,16,1874730) (# 13356) with respect to smaller t
• supplementary design of 6-(32,16,3437005) (# 13360) with respect to smaller t
• Tran van Trung construction (left) for 5-(31,16,2726880) (# 13362) : der= 5-(31,15,1874730) and res= 5-(31,16,2726880) - the given design is the residual.

# 6507: 5-(24,9,1374)

• clan: 11-(30,15,1374), 6 times derived
• $PGL(2,23)$ (>1 isomorphism types)

# 6508: 5-(25,10,5496)

• clan: 11-(30,15,1374), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1374) (# 6507) : der= 5-(24,9,1374) and res= 5-(24,10,4122) - the given design is the derived.

# 6509: 5-(24,9,138)

• clan: 11-(30,15,138), 6 times derived
• $PGL(2,23)$ (>1 isomorphism types)

# 6510: 5-(25,10,552)

• clan: 11-(30,15,138), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,138) (# 6509) : der= 5-(24,9,138) and res= 5-(24,10,414) - the given design is the derived.

# 6511: 5-(24,9,1380)

• clan: 13-(32,16,345), 7 times derived, 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6512: 5-(25,9,1725)

• clan: 13-(32,16,345), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1380) (# 6511) : der= 5-(24,8,345) and res= 5-(24,9,1380) - the given design is the residual.

# 6513: 5-(25,10,5520)

• clan: 13-(32,16,345), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1380) (# 6511) : der= 5-(24,9,1380) and res= 5-(24,10,4140) - the given design is the derived.

# 6514: 5-(26,10,7245)

• clan: 13-(32,16,345), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1725) (# 6512) : der= 5-(25,9,1725) and res= 5-(25,10,5520) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5520) (# 6513) : der= 5-(25,9,1725) and res= 5-(25,10,5520) - the given design is the residual.

# 6515: 5-(24,9,1386)

• clan: 11-(30,15,1386), 6 times derived
• $PGL(2,23)$ (>1 isomorphism types)

# 6516: 5-(25,10,5544)

• clan: 11-(30,15,1386), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1386) (# 6515) : der= 5-(24,9,1386) and res= 5-(24,10,4158) - the given design is the derived.

# 6517: 5-(26,11,19404)

• clan: 11-(30,15,1386), 2 times reduced t, 4 times derived
• Tran van Trung construction (right) for 5-(25,10,5544) (# 6516) : der= 5-(25,10,5544) and res= 5-(25,11,13860) - the given design is the derived.

# 6518: 5-(27,12,60984)

• clan: 11-(30,15,1386), 3 times reduced t, 3 times derived
• Tran van Trung construction (right) for 5-(26,11,19404) (# 6517) : der= 5-(26,11,19404) and res= 5-(26,12,41580) - the given design is the derived.

# 6519: 5-(28,13,175329)

• clan: 11-(30,15,1386), 4 times reduced t, 2 times derived
• Tran van Trung construction (right) for 5-(27,12,60984) (# 6518) : der= 5-(27,12,60984) and res= 5-(27,13,114345) - the given design is the derived.

# 6520: 5-(29,14,467544)

• clan: 11-(30,15,1386), 5 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(28,13,175329) (# 6519) : der= 5-(28,13,175329) and res= 5-(28,14,292215) - the given design is the derived.

# 6521: 5-(30,15,1168860)

• clan: 11-(30,15,1386), 6 times reduced t
• Tran van Trung construction with complementary design for 5-(29,14,467544) (# 6520)

# 6522: 5-(24,9,1392)

• clan: 13-(32,16,348), 7 times derived, 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6523: 5-(25,9,1740)

• clan: 13-(32,16,348), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1392) (# 6522) : der= 5-(24,8,348) and res= 5-(24,9,1392) - the given design is the residual.
• derived from 6-(26,10,1740) (# 14052)
• derived from supplementary of 6-(26,10,3105) (# 14055)

# 6524: 5-(25,10,5568)

• clan: 13-(32,16,348), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1392) (# 6522) : der= 5-(24,9,1392) and res= 5-(24,10,4176) - the given design is the derived.
• residual design of 6-(26,10,1740) (# 14052)
• derived from 6-(26,11,5568) (# 14053)
• residual design of supplementary of 6-(26,10,3105) (# 14055)
• derived from supplementary of 6-(26,11,9936) (# 14056)

# 6525: 5-(26,10,7308)

• clan: 13-(32,16,348), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1740) (# 6523) : der= 5-(25,9,1740) and res= 5-(25,10,5568) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5568) (# 6524) : der= 5-(25,9,1740) and res= 5-(25,10,5568) - the given design is the residual.
• derived from 6-(27,11,7308) (# 10695)
• design 6-(26,10,1740) (# 14052) with respect to smaller t
• derived from supplementary of 6-(27,11,13041) (# 14054)
• supplementary design of 6-(26,10,3105) (# 14055) with respect to smaller t

# 6526: 5-(24,9,1398)

• clan: 11-(30,15,1398), 6 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6527: 5-(25,10,5592)

• clan: 11-(30,15,1398), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1398) (# 6526) : der= 5-(24,9,1398) and res= 5-(24,10,4194) - the given design is the derived.

# 6528: 5-(24,9,1404)

• clan: 13-(32,16,351), 7 times derived, 1 times residual
• $PGL(2,23)$ (>1 isomorphism types)

# 6529: 5-(25,9,1755)

• clan: 13-(32,16,351), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1404) (# 6528) : der= 5-(24,8,351) and res= 5-(24,9,1404) - the given design is the residual.
• derived from 6-(26,10,1755) (# 14063)
• derived from supplementary of 6-(26,10,3090) (# 14066)

# 6530: 5-(25,10,5616)

• clan: 13-(32,16,351), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1404) (# 6528) : der= 5-(24,9,1404) and res= 5-(24,10,4212) - the given design is the derived.
• residual design of 6-(26,10,1755) (# 14063)
• derived from 6-(26,11,5616) (# 14064)
• residual design of supplementary of 6-(26,10,3090) (# 14066)
• derived from supplementary of 6-(26,11,9888) (# 14067)

# 6531: 5-(26,10,7371)

• clan: 13-(32,16,351), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1755) (# 6529) : der= 5-(25,9,1755) and res= 5-(25,10,5616) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5616) (# 6530) : der= 5-(25,9,1755) and res= 5-(25,10,5616) - the given design is the residual.
• derived from 6-(27,11,7371) (# 14062)
• design 6-(26,10,1755) (# 14063) with respect to smaller t
• derived from supplementary of 6-(27,11,12978) (# 14065)
• supplementary design of 6-(26,10,3090) (# 14066) with respect to smaller t

# 6532: 5-(24,9,1410)

• clan: 11-(30,15,1410), 6 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6533: 5-(25,10,5640)

• clan: 11-(30,15,1410), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1410) (# 6532) : der= 5-(24,9,1410) and res= 5-(24,10,4230) - the given design is the derived.

# 6534: 5-(24,9,1416)

• clan: 13-(32,16,354), 7 times derived, 1 times residual
• $PGL(2,23)$ (>1 isomorphism types)

# 6535: 5-(25,9,1770)

• clan: 13-(32,16,354), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1416) (# 6534) : der= 5-(24,8,354) and res= 5-(24,9,1416) - the given design is the residual.

# 6536: 5-(25,10,5664)

• clan: 13-(32,16,354), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1416) (# 6534) : der= 5-(24,9,1416) and res= 5-(24,10,4248) - the given design is the derived.

# 6537: 5-(26,10,7434)

• clan: 13-(32,16,354), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1770) (# 6535) : der= 5-(25,9,1770) and res= 5-(25,10,5664) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5664) (# 6536) : der= 5-(25,9,1770) and res= 5-(25,10,5664) - the given design is the residual.

# 6538: 5-(24,9,1422)

• clan: 11-(30,15,1422), 6 times derived
• $PGL(2,23)$ (>1 isomorphism types)

# 6539: 5-(25,10,5688)

• clan: 11-(30,15,1422), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1422) (# 6538) : der= 5-(24,9,1422) and res= 5-(24,10,4266) - the given design is the derived.

# 6540: 5-(24,9,1428)

• clan: 17-(36,18,7), 9 times derived, 3 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• residual design of 6-(25,9,357) (# 13776)
• residual design of supplementary of 6-(25,9,612) (# 13779)

# 6541: 5-(25,9,1785)

• clan: 17-(36,18,7), 1 times reduced t, 9 times derived, 2 times residual
• Tran van Trung construction (left) for 5-(24,9,1428) (# 6540) : der= 5-(24,8,357) and res= 5-(24,9,1428) - the given design is the residual.
• residual design of 6-(26,9,420) (# 10580)
• design 6-(25,9,357) (# 13776) with respect to smaller t
• residual design of supplementary of 6-(26,9,720) (# 13777)
• supplementary design of 6-(25,9,612) (# 13779) with respect to smaller t
• derived from 6-(26,10,1785) (# 13791)
• derived from supplementary of 6-(26,10,3060) (# 13792)

# 6542: 5-(25,10,5712)

• clan: 17-(36,18,7), 1 times reduced t, 8 times derived, 3 times residual
• Tran van Trung construction (right) for 5-(24,9,1428) (# 6540) : der= 5-(24,9,1428) and res= 5-(24,10,4284) - the given design is the derived.
• residual design of 6-(26,10,1785) (# 13791)
• residual design of supplementary of 6-(26,10,3060) (# 13792)
• derived from 6-(26,11,5712) (# 14096)
• derived from supplementary of 6-(26,11,9792) (# 14098)

# 6543: 5-(26,9,2205)

• clan: 17-(36,18,7), 2 times reduced t, 9 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(25,9,1785) (# 6541) : der= 5-(25,8,420) and res= 5-(25,9,1785) - the given design is the residual.
• $PGL(2,25)$
• design 6-(26,9,420) (# 10580) with respect to smaller t
• residual design of 6-(27,9,490) (# 10583)
• derived from 6-(27,10,2205) (# 10595)
• derived from supplementary of 6-(27,10,3780) (# 10601)
• supplementary design of 6-(26,9,720) (# 13777) with respect to smaller t

# 6544: 5-(26,10,7497)

• clan: 17-(36,18,7), 2 times reduced t, 8 times derived, 2 times residual
• Tran van Trung construction (right) for 5-(25,9,1785) (# 6541) : der= 5-(25,9,1785) and res= 5-(25,10,5712) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5712) (# 6542) : der= 5-(25,9,1785) and res= 5-(25,10,5712) - the given design is the residual.
• residual design of 6-(27,10,2205) (# 10595)
• residual design of supplementary of 6-(27,10,3780) (# 10601)
• derived from 6-(27,11,7497) (# 10701)
• design 6-(26,10,1785) (# 13791) with respect to smaller t
• supplementary design of 6-(26,10,3060) (# 13792) with respect to smaller t
• derived from supplementary of 6-(27,11,12852) (# 14097)

# 6545: 5-(27,9,2695)

• clan: 17-(36,18,7), 3 times reduced t, 9 times derived
• Tran van Trung construction (left) for 5-(26,9,2205) (# 6543) : der= 5-(26,8,490) and res= 5-(26,9,2205) - the given design is the residual.
• $PGL(2,25)+$
• design 6-(27,9,490) (# 10583) with respect to smaller t
• derived from 6-(28,10,2695) (# 10598)

# 6546: 5-(27,10,9702)

• clan: 17-(36,18,7), 3 times reduced t, 8 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(26,9,2205) (# 6543) : der= 5-(26,9,2205) and res= 5-(26,10,7497) - the given design is the derived.
• Tran van Trung construction (left) for 5-(26,10,7497) (# 6544) : der= 5-(26,9,2205) and res= 5-(26,10,7497) - the given design is the residual.
• design 6-(27,10,2205) (# 10595) with respect to smaller t
• residual design of 6-(28,10,2695) (# 10598)
• supplementary design of 6-(27,10,3780) (# 10601) with respect to smaller t
• derived from 6-(28,11,9702) (# 10706)
• derived from supplementary of 6-(28,11,16632) (# 14102)

# 6547: 5-(28,10,12397)

• clan: 17-(36,18,7), 4 times reduced t, 8 times derived
• Tran van Trung construction (right) for 5-(27,9,2695) (# 6545) : der= 5-(27,9,2695) and res= 5-(27,10,9702) - the given design is the derived.
• Tran van Trung construction (left) for 5-(27,10,9702) (# 6546) : der= 5-(27,9,2695) and res= 5-(27,10,9702) - the given design is the residual.
• design 6-(28,10,2695) (# 10598) with respect to smaller t
• derived from 6-(29,11,12397) (# 10709)

# 6548: 5-(24,9,1434)

• clan: 11-(30,15,1434), 6 times derived
• $PGL(2,23)$ (>1 isomorphism types)

# 6549: 5-(25,10,5736)

• clan: 11-(30,15,1434), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1434) (# 6548) : der= 5-(24,9,1434) and res= 5-(24,10,4302) - the given design is the derived.

# 6550: 5-(26,11,20076)

• clan: 11-(30,15,1434), 2 times reduced t, 4 times derived
• Tran van Trung construction (right) for 5-(25,10,5736) (# 6549) : der= 5-(25,10,5736) and res= 5-(25,11,14340) - the given design is the derived.

# 6551: 5-(27,12,63096)

• clan: 11-(30,15,1434), 3 times reduced t, 3 times derived
• Tran van Trung construction (right) for 5-(26,11,20076) (# 6550) : der= 5-(26,11,20076) and res= 5-(26,12,43020) - the given design is the derived.

# 6552: 5-(28,13,181401)

• clan: 11-(30,15,1434), 4 times reduced t, 2 times derived
• Tran van Trung construction (right) for 5-(27,12,63096) (# 6551) : der= 5-(27,12,63096) and res= 5-(27,13,118305) - the given design is the derived.

# 6553: 5-(29,14,483736)

• clan: 11-(30,15,1434), 5 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(28,13,181401) (# 6552) : der= 5-(28,13,181401) and res= 5-(28,14,302335) - the given design is the derived.

# 6554: 5-(30,15,1209340)

• clan: 11-(30,15,1434), 6 times reduced t
• Tran van Trung construction with complementary design for 5-(29,14,483736) (# 6553)

# 6555: 5-(24,9,144)

• clan: 13-(32,16,36), 7 times derived, 1 times residual
• $PGL(2,23)$ (>1 isomorphism types)

# 6556: 5-(25,9,180)

• clan: 13-(32,16,36), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,144) (# 6555) : der= 5-(24,8,36) and res= 5-(24,9,144) - the given design is the residual.

# 6557: 5-(25,10,576)

• clan: 13-(32,16,36), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,144) (# 6555) : der= 5-(24,9,144) and res= 5-(24,10,432) - the given design is the derived.

# 6558: 5-(26,10,756)

• clan: 13-(32,16,36), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,180) (# 6556) : der= 5-(25,9,180) and res= 5-(25,10,576) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,576) (# 6557) : der= 5-(25,9,180) and res= 5-(25,10,576) - the given design is the residual.

# 6559: 5-(24,9,1440)

• clan: 13-(32,16,360), 7 times derived, 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• residual design of 6-(25,9,360) (# 10446)

# 6560: 5-(25,9,1800)

• clan: 13-(32,16,360), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1440) (# 6559) : der= 5-(24,8,360) and res= 5-(24,9,1440) - the given design is the residual.
• design 6-(25,9,360) (# 10446) with respect to smaller t
• derived from 6-(26,10,1800) (# 10515)

# 6561: 5-(25,10,5760)

• clan: 13-(32,16,360), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1440) (# 6559) : der= 5-(24,9,1440) and res= 5-(24,10,4320) - the given design is the derived.
• residual design of 6-(26,10,1800) (# 10515)

# 6562: 5-(26,10,7560)

• clan: 13-(32,16,360), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1800) (# 6560) : der= 5-(25,9,1800) and res= 5-(25,10,5760) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5760) (# 6561) : der= 5-(25,9,1800) and res= 5-(25,10,5760) - the given design is the residual.
• design 6-(26,10,1800) (# 10515) with respect to smaller t

# 6563: 5-(24,9,1446)

• clan: 11-(30,15,1446), 6 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6564: 5-(25,10,5784)

• clan: 11-(30,15,1446), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1446) (# 6563) : der= 5-(24,9,1446) and res= 5-(24,10,4338) - the given design is the derived.

# 6565: 5-(24,9,1452)

• clan: 13-(32,16,363), 7 times derived, 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6566: 5-(25,9,1815)

• clan: 13-(32,16,363), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1452) (# 6565) : der= 5-(24,8,363) and res= 5-(24,9,1452) - the given design is the residual.

# 6567: 5-(25,10,5808)

• clan: 13-(32,16,363), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1452) (# 6565) : der= 5-(24,9,1452) and res= 5-(24,10,4356) - the given design is the derived.

# 6568: 5-(26,10,7623)

• clan: 13-(32,16,363), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1815) (# 6566) : der= 5-(25,9,1815) and res= 5-(25,10,5808) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5808) (# 6567) : der= 5-(25,9,1815) and res= 5-(25,10,5808) - the given design is the residual.

# 6569: 5-(26,11,20328)

• clan: 13-(32,16,363), 2 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(25,10,5808) (# 6567) : der= 5-(25,10,5808) and res= 5-(25,11,14520) - the given design is the derived.

# 6570: 5-(27,11,27951)

• clan: 13-(32,16,363), 3 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(26,10,7623) (# 6568) : der= 5-(26,10,7623) and res= 5-(26,11,20328) - the given design is the derived.
• Tran van Trung construction (left) for 5-(26,11,20328) (# 6569) : der= 5-(26,10,7623) and res= 5-(26,11,20328) - the given design is the residual.

# 6571: 5-(27,12,63888)

• clan: 13-(32,16,363), 3 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(26,11,20328) (# 6569) : der= 5-(26,11,20328) and res= 5-(26,12,43560) - the given design is the derived.

# 6572: 5-(28,12,91839)

• clan: 13-(32,16,363), 4 times reduced t, 4 times derived
• Tran van Trung construction (right) for 5-(27,11,27951) (# 6570) : der= 5-(27,11,27951) and res= 5-(27,12,63888) - the given design is the derived.
• Tran van Trung construction (left) for 5-(27,12,63888) (# 6571) : der= 5-(27,11,27951) and res= 5-(27,12,63888) - the given design is the residual.

# 6573: 5-(28,13,183678)

• clan: 13-(32,16,363), 4 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(27,12,63888) (# 6571) : der= 5-(27,12,63888) and res= 5-(27,13,119790) - the given design is the derived.

# 6574: 5-(29,13,275517)

• clan: 13-(32,16,363), 5 times reduced t, 3 times derived
• Tran van Trung construction (right) for 5-(28,12,91839) (# 6572) : der= 5-(28,12,91839) and res= 5-(28,13,183678) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,13,183678) (# 6573) : der= 5-(28,12,91839) and res= 5-(28,13,183678) - the given design is the residual.

# 6575: 5-(29,14,489808)

• clan: 13-(32,16,363), 5 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(28,13,183678) (# 6573) : der= 5-(28,13,183678) and res= 5-(28,14,306130) - the given design is the derived.

# 6576: 5-(30,14,765325)

• clan: 13-(32,16,363), 6 times reduced t, 2 times derived
• Tran van Trung construction (right) for 5-(29,13,275517) (# 6574) : der= 5-(29,13,275517) and res= 5-(29,14,489808) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,14,489808) (# 6575) : der= 5-(29,13,275517) and res= 5-(29,14,489808) - the given design is the residual.

# 6577: 5-(30,15,1224520)

• clan: 13-(32,16,363), 6 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(29,14,489808) (# 6575)

# 6578: 5-(31,15,1989845)

• clan: 13-(32,16,363), 7 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(30,14,765325) (# 6576) : der= 5-(30,14,765325) and res= 5-(30,15,1224520) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,15,1224520) (# 6577) : der= 5-(30,14,765325) and res= 5-(30,15,1224520) - the given design is the residual.

# 6579: 5-(32,16,4884165)

• clan: 13-(32,16,363), 8 times reduced t
• Tran van Trung construction with complementary design for 5-(31,15,1989845) (# 6578)

# 6580: 5-(24,9,1458)

• clan: 11-(30,15,1458), 6 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6581: 5-(25,10,5832)

• clan: 11-(30,15,1458), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1458) (# 6580) : der= 5-(24,9,1458) and res= 5-(24,10,4374) - the given design is the derived.
• derived from 6-(26,11,5832) (# 14790)
• derived from supplementary of 6-(26,11,9672) (# 14793)

# 6582: 5-(24,9,1464)

• clan: 13-(32,16,366), 7 times derived, 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6583: 5-(25,9,1830)

• clan: 13-(32,16,366), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1464) (# 6582) : der= 5-(24,8,366) and res= 5-(24,9,1464) - the given design is the residual.

# 6584: 5-(25,10,5856)

• clan: 13-(32,16,366), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1464) (# 6582) : der= 5-(24,9,1464) and res= 5-(24,10,4392) - the given design is the derived.

# 6585: 5-(26,10,7686)

• clan: 13-(32,16,366), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1830) (# 6583) : der= 5-(25,9,1830) and res= 5-(25,10,5856) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5856) (# 6584) : der= 5-(25,9,1830) and res= 5-(25,10,5856) - the given design is the residual.

# 6586: 5-(24,9,1470)

• clan: 11-(30,15,1470), 6 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6587: 5-(25,10,5880)

• clan: 11-(30,15,1470), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1470) (# 6586) : der= 5-(24,9,1470) and res= 5-(24,10,4410) - the given design is the derived.

# 6588: 5-(24,9,1476)

• clan: 13-(32,16,369), 7 times derived, 1 times residual
• $PGL(2,23)$ (>1 isomorphism types)
• residual design of 6-(25,9,369) (# 10449)

# 6589: 5-(25,9,1845)

• clan: 13-(32,16,369), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1476) (# 6588) : der= 5-(24,8,369) and res= 5-(24,9,1476) - the given design is the residual.
• design 6-(25,9,369) (# 10449) with respect to smaller t
• derived from 6-(26,10,1845) (# 10518)
• derived from supplementary of 6-(26,10,3000) (# 14106)

# 6590: 5-(25,10,5904)

• clan: 13-(32,16,369), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1476) (# 6588) : der= 5-(24,9,1476) and res= 5-(24,10,4428) - the given design is the derived.
• residual design of 6-(26,10,1845) (# 10518)
• derived from 6-(26,11,5904) (# 14104)
• residual design of supplementary of 6-(26,10,3000) (# 14106)
• derived from supplementary of 6-(26,11,9600) (# 14107)

# 6591: 5-(26,10,7749)

• clan: 13-(32,16,369), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1845) (# 6589) : der= 5-(25,9,1845) and res= 5-(25,10,5904) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5904) (# 6590) : der= 5-(25,9,1845) and res= 5-(25,10,5904) - the given design is the residual.
• design 6-(26,10,1845) (# 10518) with respect to smaller t
• derived from 6-(27,11,7749) (# 10712)
• derived from supplementary of 6-(27,11,12600) (# 14105)
• supplementary design of 6-(26,10,3000) (# 14106) with respect to smaller t

# 6592: 5-(24,9,1482)

• clan: 13-(30,15,52), 2 times reduced t, 6 times derived
• $PGL(2,23)$ (>1 isomorphism types)

# 6593: 5-(25,10,5928)

• clan: 13-(30,15,52), 3 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1482) (# 6592) : der= 5-(24,9,1482) and res= 5-(24,10,4446) - the given design is the derived.

# 6594: 5-(24,9,1488)

• clan: 13-(32,16,372), 7 times derived, 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6595: 5-(25,9,1860)

• clan: 13-(32,16,372), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 5-(24,9,1488) (# 6594) : der= 5-(24,8,372) and res= 5-(24,9,1488) - the given design is the residual.
• derived from 6-(26,10,1860) (# 14112)
• derived from supplementary of 6-(26,10,2985) (# 14115)

# 6596: 5-(25,10,5952)

• clan: 13-(32,16,372), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(24,9,1488) (# 6594) : der= 5-(24,9,1488) and res= 5-(24,10,4464) - the given design is the derived.
• residual design of 6-(26,10,1860) (# 14112)
• derived from 6-(26,11,5952) (# 14113)
• residual design of supplementary of 6-(26,10,2985) (# 14115)
• derived from supplementary of 6-(26,11,9552) (# 14116)

# 6597: 5-(26,10,7812)

• clan: 13-(32,16,372), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 5-(25,9,1860) (# 6595) : der= 5-(25,9,1860) and res= 5-(25,10,5952) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,5952) (# 6596) : der= 5-(25,9,1860) and res= 5-(25,10,5952) - the given design is the residual.
• derived from 6-(27,11,7812) (# 14111)
• design 6-(26,10,1860) (# 14112) with respect to smaller t
• derived from supplementary of 6-(27,11,12537) (# 14114)
• supplementary design of 6-(26,10,2985) (# 14115) with respect to smaller t

# 6598: 5-(24,9,1494)

• clan: 11-(30,15,1494), 6 times derived
• $PGL(2,23)$ (>1 isomorphism types)

# 6599: 5-(25,10,5976)

• clan: 11-(30,15,1494), 1 times reduced t, 5 times derived
• Tran van Trung construction (right) for 5-(24,9,1494) (# 6598) : der= 5-(24,9,1494) and res= 5-(24,10,4482) - the given design is the derived.

created: Fri Oct 23 11:10:19 CEST 2009