t designs with small t, id ge 17800

• clan: 13-(32,16,699), 2 times derived, 5 times residual
• residual design of supplementary of 7-(26,14,14040) (# 17793)
• residual design of 7-(26,14,36348) (# 17794)

# 17801: 7-(30,14,68310)

• clan: 13-(32,16,270), 4 times reduced t, 2 times derived
• Tran van Trung construction (right) for 7-(29,13,20790) (# 17796) : der= 7-(29,13,20790) and res= 7-(29,14,47520) - the given design is the derived.

# 17802: 5-(24,14,25740)

• clan: 13-(32,16,270), 2 times derived, 6 times residual
• residual design of 6-(25,14,21060) (# 17799)
• residual design of supplementary of 6-(25,14,54522) (# 17800)

# 17803: 5-(24,14,66638)

• clan: 13-(32,16,699), 2 times derived, 6 times residual
• residual design of supplementary of 6-(25,14,21060) (# 17799)
• residual design of 6-(25,14,54522) (# 17800)

# 17804: 7-(31,15,204930)

• clan: 13-(32,16,270), 5 times reduced t, 1 times derived
• Tran van Trung construction (right) for 7-(30,14,68310) (# 17801) : der= 7-(30,14,68310) and res= 7-(30,15,136620) - the given design is the derived.

# 17805: 8-(27,13,4608)

• clan: 13-(32,16,384), 3 times derived, 2 times residual
• $ASL(3,3)$ $\ge 200000000$ isomorphism types
• derived from 9-(28,14,4608) (# 17810)
• derived from supplementary of 9-(28,14,7020) (# 17840)

# 17806: 7-(27,13,15360)

• clan: 13-(32,16,384), 1 times reduced t, 3 times derived, 2 times residual
• design 8-(27,13,4608) (# 17805) with respect to smaller t
• Tran van Trung construction (right) for 7-(26,12,4608) (# 17807) : der= 7-(26,12,4608) and res= 7-(26,13,10752) - the given design is the derived.
• Tran van Trung construction (left) for 7-(26,13,10752) (# 17808) : der= 7-(26,12,4608) and res= 7-(26,13,10752) - the given design is the residual.
• derived from 8-(28,14,15360) (# 17809)
• derived from supplementary of 8-(28,14,23400) (# 17826)
• supplementary design of 8-(27,13,7020) (# 17827) with respect to smaller t

# 17807: 7-(26,12,4608)

• clan: 13-(32,16,384), 4 times derived, 2 times residual
• derived from 8-(27,13,4608) (# 17805)
• derived from supplementary of 8-(27,13,7020) (# 17827)

# 17808: 7-(26,13,10752)

• clan: 13-(32,16,384), 3 times derived, 3 times residual
• residual design of 8-(27,13,4608) (# 17805)
• Alltop construction for design 6-(25,12,10752) (# 17818)
• derived from 8-(27,14,10752) (# 17825)
• residual design of supplementary of 8-(27,13,7020) (# 17827)
• derived from supplementary of 8-(27,14,16380) (# 17828)

# 17809: 8-(28,14,15360)

• clan: 13-(32,16,384), 1 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 8-(27,13,4608) (# 17805)
• design 9-(28,14,4608) (# 17810) with respect to smaller t
• Tran van Trung construction (left) for 8-(27,14,10752) (# 17825) : der= 8-(27,13,4608) and res= 8-(27,14,10752) - the given design is the residual.
• supplementary design of 9-(28,14,7020) (# 17840) with respect to smaller t
• red 9-(28,14,4608) ($\ge 1.6\times 10^{16}$ isomorphism types)

# 17810: 9-(28,14,4608)

• clan: 13-(32,16,384), 2 times derived, 2 times residual
• Alltop construction for design 8-(27,13,4608) (# 17805)

# 17811: 7-(27,13,23400)

• clan: 13-(32,16,585), 1 times reduced t, 3 times derived, 2 times residual
• supplementary design of 8-(27,13,4608) (# 17805) with respect to smaller t
• derived from supplementary of 8-(28,14,15360) (# 17809)
• Tran van Trung construction (right) for 7-(26,12,7020) (# 17812) : der= 7-(26,12,7020) and res= 7-(26,13,16380) - the given design is the derived.
• Tran van Trung construction (left) for 7-(26,13,16380) (# 17813) : der= 7-(26,12,7020) and res= 7-(26,13,16380) - the given design is the residual.
• derived from 8-(28,14,23400) (# 17826)
• design 8-(27,13,7020) (# 17827) with respect to smaller t

# 17812: 7-(26,12,7020)

• clan: 13-(32,16,585), 4 times derived, 2 times residual
• derived from supplementary of 8-(27,13,4608) (# 17805)
• derived from 8-(27,13,7020) (# 17827)

# 17813: 7-(26,13,16380)

• clan: 13-(32,16,585), 3 times derived, 3 times residual
• residual design of supplementary of 8-(27,13,4608) (# 17805)
• Alltop construction for design 6-(25,12,16380) (# 17819)
• derived from supplementary of 8-(27,14,10752) (# 17825)
• residual design of 8-(27,13,7020) (# 17827)
• derived from 8-(27,14,16380) (# 17828)

# 17814: 6-(26,12,15360)

• clan: 13-(32,16,384), 1 times reduced t, 4 times derived, 2 times residual
• derived from 7-(27,13,15360) (# 17806)
• design 7-(26,12,4608) (# 17807) with respect to smaller t
• derived from supplementary of 7-(27,13,23400) (# 17811)
• supplementary design of 7-(26,12,7020) (# 17812) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,12,10752) (# 17818) : der= 6-(25,11,4608) and res= 6-(25,12,10752) - the given design is the residual.
• residual design of 7-(27,12,6144) (# 17820)

# 17815: 6-(26,13,30720)

• clan: 13-(32,16,384), 1 times reduced t, 3 times derived, 3 times residual
• residual design of 7-(27,13,15360) (# 17806)
• design 7-(26,13,10752) (# 17808) with respect to smaller t
• residual design of supplementary of 7-(27,13,23400) (# 17811)
• supplementary design of 7-(26,13,16380) (# 17813) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(25,12,10752) (# 17818)
• Tran van Trung construction (right) for 6-(25,12,10752) (# 17818) : der= 6-(25,12,10752) and res= 6-(25,13,19968) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,13,19968) (# 17821) : der= 6-(25,12,10752) and res= 6-(25,13,19968) - the given design is the residual.
• derived from 7-(27,14,30720) (# 17823)
• derived from supplementary of 7-(27,14,46800) (# 17824)

# 17816: 6-(26,12,23400)

• clan: 13-(32,16,585), 1 times reduced t, 4 times derived, 2 times residual
• derived from supplementary of 7-(27,13,15360) (# 17806)
• supplementary design of 7-(26,12,4608) (# 17807) with respect to smaller t
• derived from 7-(27,13,23400) (# 17811)
• design 7-(26,12,7020) (# 17812) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,12,16380) (# 17819) : der= 6-(25,11,7020) and res= 6-(25,12,16380) - the given design is the residual.
• residual design of supplementary of 7-(27,12,6144) (# 17820)

# 17817: 6-(26,13,46800)

• clan: 13-(32,16,585), 1 times reduced t, 3 times derived, 3 times residual
• residual design of supplementary of 7-(27,13,15360) (# 17806)
• supplementary design of 7-(26,13,10752) (# 17808) with respect to smaller t
• residual design of 7-(27,13,23400) (# 17811)
• design 7-(26,13,16380) (# 17813) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(25,12,16380) (# 17819)
• Tran van Trung construction (right) for 6-(25,12,16380) (# 17819) : der= 6-(25,12,16380) and res= 6-(25,13,30420) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,13,30420) (# 17822) : der= 6-(25,12,16380) and res= 6-(25,13,30420) - the given design is the residual.
• derived from supplementary of 7-(27,14,30720) (# 17823)
• derived from 7-(27,14,46800) (# 17824)

# 17818: 6-(25,12,10752)

• clan: 13-(32,16,384), 4 times derived, 3 times residual
• residual design of 7-(26,12,4608) (# 17807)
• derived from 7-(26,13,10752) (# 17808)
• residual design of supplementary of 7-(26,12,7020) (# 17812)
• derived from supplementary of 7-(26,13,16380) (# 17813)

# 17819: 6-(25,12,16380)

• clan: 13-(32,16,585), 4 times derived, 3 times residual
• residual design of supplementary of 7-(26,12,4608) (# 17807)
• derived from supplementary of 7-(26,13,10752) (# 17808)
• residual design of 7-(26,12,7020) (# 17812)
• derived from 7-(26,13,16380) (# 17813)

# 17820: 7-(27,12,6144)

• clan: 13-(32,16,384), 1 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (left) for 7-(26,12,4608) (# 17807) : der= 7-(26,11,1536) and res= 7-(26,12,4608) - the given design is the residual.

# 17821: 6-(25,13,19968)

• clan: 13-(32,16,384), 3 times derived, 4 times residual
• residual design of 7-(26,13,10752) (# 17808)
• residual design of supplementary of 7-(26,13,16380) (# 17813)
• derived from 7-(26,14,19968) (# 17838)
• derived from supplementary of 7-(26,14,30420) (# 17839)

# 17822: 6-(25,13,30420)

• clan: 13-(32,16,585), 3 times derived, 4 times residual
• residual design of supplementary of 7-(26,13,10752) (# 17808)
• residual design of 7-(26,13,16380) (# 17813)
• derived from supplementary of 7-(26,14,19968) (# 17838)
• derived from 7-(26,14,30420) (# 17839)

# 17823: 7-(27,14,30720)

• clan: 13-(32,16,384), 1 times reduced t, 2 times derived, 3 times residual
• residual design of 8-(28,14,15360) (# 17809)
• design 8-(27,14,10752) (# 17825) with respect to smaller t
• residual design of supplementary of 8-(28,14,23400) (# 17826)
• supplementary design of 8-(27,14,16380) (# 17828) with respect to smaller t
• Tran van Trung construction (left) for 7-(26,14,19968) (# 17838) : der= 7-(26,13,10752) and res= 7-(26,14,19968) - the given design is the residual.

# 17824: 7-(27,14,46800)

• clan: 13-(32,16,585), 1 times reduced t, 2 times derived, 3 times residual
• residual design of supplementary of 8-(28,14,15360) (# 17809)
• supplementary design of 8-(27,14,10752) (# 17825) with respect to smaller t
• residual design of 8-(28,14,23400) (# 17826)
• design 8-(27,14,16380) (# 17828) with respect to smaller t
• Tran van Trung construction (left) for 7-(26,14,30420) (# 17839) : der= 7-(26,13,16380) and res= 7-(26,14,30420) - the given design is the residual.

# 17825: 8-(27,14,10752)

• clan: 13-(32,16,384), 2 times derived, 3 times residual
• residual design of 9-(28,14,4608) (# 17810)
• residual design of supplementary of 9-(28,14,7020) (# 17840)

# 17826: 8-(28,14,23400)

• clan: 13-(32,16,585), 1 times reduced t, 2 times derived, 2 times residual
• supplementary design of 9-(28,14,4608) (# 17810) with respect to smaller t
• Tran van Trung construction with complementary design for 8-(27,13,7020) (# 17827)
• Tran van Trung construction (right) for 8-(27,13,7020) (# 17827) : der= 8-(27,13,7020) and res= 8-(27,14,16380) - the given design is the derived.
• Tran van Trung construction (left) for 8-(27,14,16380) (# 17828) : der= 8-(27,13,7020) and res= 8-(27,14,16380) - the given design is the residual.
• design 9-(28,14,7020) (# 17840) with respect to smaller t

# 17827: 8-(27,13,7020)

• clan: 13-(32,16,585), 3 times derived, 2 times residual
• derived from supplementary of 9-(28,14,4608) (# 17810)
• derived from 9-(28,14,7020) (# 17840)

# 17828: 8-(27,14,16380)

• clan: 13-(32,16,585), 2 times derived, 3 times residual
• residual design of supplementary of 9-(28,14,4608) (# 17810)
• residual design of 9-(28,14,7020) (# 17840)

# 17829: 5-(25,12,46800)

• clan: 13-(32,16,585), 1 times reduced t, 4 times derived, 3 times residual
• residual design of supplementary of 6-(26,12,15360) (# 17814)
• derived from supplementary of 6-(26,13,30720) (# 17815)
• residual design of 6-(26,12,23400) (# 17816)
• derived from 6-(26,13,46800) (# 17817)
• supplementary design of 6-(25,12,10752) (# 17818) with respect to smaller t
• design 6-(25,12,16380) (# 17819) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,12,30420) (# 17832) : der= 5-(24,11,16380) and res= 5-(24,12,30420) - the given design is the residual.

# 17830: 5-(25,13,49920)

• clan: 13-(32,16,384), 1 times reduced t, 3 times derived, 4 times residual
• residual design of 6-(26,13,30720) (# 17815)
• residual design of supplementary of 6-(26,13,46800) (# 17817)
• design 6-(25,13,19968) (# 17821) with respect to smaller t
• supplementary design of 6-(25,13,30420) (# 17822) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,13,29952) (# 17834) : der= 5-(24,12,19968) and res= 5-(24,13,29952) - the given design is the residual.
• derived from 6-(26,14,49920) (# 17836)
• derived from supplementary of 6-(26,14,76050) (# 17837)

# 17831: 5-(25,13,76050)

• clan: 13-(32,16,585), 1 times reduced t, 3 times derived, 4 times residual
• residual design of supplementary of 6-(26,13,30720) (# 17815)
• residual design of 6-(26,13,46800) (# 17817)
• supplementary design of 6-(25,13,19968) (# 17821) with respect to smaller t
• design 6-(25,13,30420) (# 17822) with respect to smaller t
• Tran van Trung construction (right) for 5-(24,12,30420) (# 17832) : der= 5-(24,12,30420) and res= 5-(24,13,45630) - the given design is the derived.
• Tran van Trung construction (left) for 5-(24,13,45630) (# 17835) : der= 5-(24,12,30420) and res= 5-(24,13,45630) - the given design is the residual.
• derived from supplementary of 6-(26,14,49920) (# 17836)
• derived from 6-(26,14,76050) (# 17837)

# 17832: 5-(24,12,30420)

• clan: 13-(32,16,585), 4 times derived, 4 times residual
• residual design of supplementary of 6-(25,12,10752) (# 17818)
• residual design of 6-(25,12,16380) (# 17819)
• derived from supplementary of 6-(25,13,19968) (# 17821)
• derived from 6-(25,13,30420) (# 17822)

# 17833: 7-(28,12,8064)

• clan: 13-(32,16,384), 2 times reduced t, 4 times derived
• Tran van Trung construction (left) for 7-(27,12,6144) (# 17820) : der= 7-(27,11,1920) and res= 7-(27,12,6144) - the given design is the residual.

# 17834: 5-(24,13,29952)

• clan: 13-(32,16,384), 3 times derived, 5 times residual
• residual design of 6-(25,13,19968) (# 17821)
• residual design of supplementary of 6-(25,13,30420) (# 17822)
• derived from 6-(25,14,29952) (# 17844)
• derived from supplementary of 6-(25,14,45630) (# 17845)

# 17835: 5-(24,13,45630)

• clan: 13-(32,16,585), 3 times derived, 5 times residual
• residual design of supplementary of 6-(25,13,19968) (# 17821)
• residual design of 6-(25,13,30420) (# 17822)
• derived from supplementary of 6-(25,14,29952) (# 17844)
• derived from 6-(25,14,45630) (# 17845)

# 17836: 6-(26,14,49920)

• clan: 13-(32,16,384), 1 times reduced t, 2 times derived, 4 times residual
• residual design of 7-(27,14,30720) (# 17823)
• residual design of supplementary of 7-(27,14,46800) (# 17824)
• design 7-(26,14,19968) (# 17838) with respect to smaller t
• supplementary design of 7-(26,14,30420) (# 17839) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,14,29952) (# 17844) : der= 6-(25,13,19968) and res= 6-(25,14,29952) - the given design is the residual.

# 17837: 6-(26,14,76050)

• clan: 13-(32,16,585), 1 times reduced t, 2 times derived, 4 times residual
• residual design of supplementary of 7-(27,14,30720) (# 17823)
• residual design of 7-(27,14,46800) (# 17824)
• supplementary design of 7-(26,14,19968) (# 17838) with respect to smaller t
• design 7-(26,14,30420) (# 17839) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,14,45630) (# 17845) : der= 6-(25,13,30420) and res= 6-(25,14,45630) - the given design is the residual.

# 17838: 7-(26,14,19968)

• clan: 13-(32,16,384), 2 times derived, 4 times residual
• residual design of 8-(27,14,10752) (# 17825)
• residual design of supplementary of 8-(27,14,16380) (# 17828)

# 17839: 7-(26,14,30420)

• clan: 13-(32,16,585), 2 times derived, 4 times residual
• residual design of supplementary of 8-(27,14,10752) (# 17825)
• residual design of 8-(27,14,16380) (# 17828)

# 17840: 9-(28,14,7020)

• clan: 13-(32,16,585), 2 times derived, 2 times residual
• Alltop construction for design 8-(27,13,7020) (# 17827)

# 17841: 7-(29,13,29568)

• clan: 13-(32,16,384), 3 times reduced t, 3 times derived
• Tran van Trung construction (right) for 7-(28,12,8064) (# 17833) : der= 7-(28,12,8064) and res= 7-(28,13,21504) - the given design is the derived.

# 17842: 5-(25,14,66560)

• clan: 13-(32,16,384), 1 times reduced t, 2 times derived, 5 times residual
• residual design of 6-(26,14,49920) (# 17836)
• residual design of supplementary of 6-(26,14,76050) (# 17837)
• design 6-(25,14,29952) (# 17844) with respect to smaller t
• supplementary design of 6-(25,14,45630) (# 17845) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,14,36608) (# 17847) : der= 5-(24,13,29952) and res= 5-(24,14,36608) - the given design is the residual.

# 17843: 5-(25,14,101400)

• clan: 13-(32,16,585), 1 times reduced t, 2 times derived, 5 times residual
• residual design of supplementary of 6-(26,14,49920) (# 17836)
• residual design of 6-(26,14,76050) (# 17837)
• supplementary design of 6-(25,14,29952) (# 17844) with respect to smaller t
• design 6-(25,14,45630) (# 17845) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,14,55770) (# 17848) : der= 5-(24,13,45630) and res= 5-(24,14,55770) - the given design is the residual.

# 17844: 6-(25,14,29952)

• clan: 13-(32,16,384), 2 times derived, 5 times residual
• residual design of 7-(26,14,19968) (# 17838)
• residual design of supplementary of 7-(26,14,30420) (# 17839)

# 17845: 6-(25,14,45630)

• clan: 13-(32,16,585), 2 times derived, 5 times residual
• residual design of supplementary of 7-(26,14,19968) (# 17838)
• residual design of 7-(26,14,30420) (# 17839)

# 17846: 7-(30,14,97152)

• clan: 13-(32,16,384), 4 times reduced t, 2 times derived
• Tran van Trung construction (right) for 7-(29,13,29568) (# 17841) : der= 7-(29,13,29568) and res= 7-(29,14,67584) - the given design is the derived.

# 17847: 5-(24,14,36608)

• clan: 13-(32,16,384), 2 times derived, 6 times residual
• residual design of 6-(25,14,29952) (# 17844)
• residual design of supplementary of 6-(25,14,45630) (# 17845)

# 17848: 5-(24,14,55770)

• clan: 13-(32,16,585), 2 times derived, 6 times residual
• residual design of supplementary of 6-(25,14,29952) (# 17844)
• residual design of 6-(25,14,45630) (# 17845)

# 17849: 7-(31,15,291456)

• clan: 13-(32,16,384), 5 times reduced t, 1 times derived
• Tran van Trung construction (right) for 7-(30,14,97152) (# 17846) : der= 7-(30,14,97152) and res= 7-(30,15,194304) - the given design is the derived.

# 17850: 8-(27,13,5076)

• clan: 13-(32,16,423), 3 times derived, 2 times residual
• $ASL(3,3)$
• derived from 9-(28,14,5076) (# 17854)
• derived from supplementary of 9-(28,14,6552) (# 17880)

# 17851: 7-(26,12,5076)

• clan: 13-(32,16,423), 4 times derived, 2 times residual
• derived from 8-(27,13,5076) (# 17850)
• derived from supplementary of 8-(27,13,6552) (# 17868)

# 17852: 7-(26,13,11844)

• clan: 13-(32,16,423), 3 times derived, 3 times residual
• residual design of 8-(27,13,5076) (# 17850)
• Alltop construction for design 6-(25,12,11844) (# 17859)
• derived from 8-(27,14,11844) (# 17866)
• residual design of supplementary of 8-(27,13,6552) (# 17868)
• derived from supplementary of 8-(27,14,15288) (# 17869)

# 17853: 8-(28,14,16920)

• clan: 13-(32,16,423), 1 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 8-(27,13,5076) (# 17850)
• design 9-(28,14,5076) (# 17854) with respect to smaller t
• Tran van Trung construction (left) for 8-(27,14,11844) (# 17866) : der= 8-(27,13,5076) and res= 8-(27,14,11844) - the given design is the residual.
• supplementary design of 9-(28,14,6552) (# 17880) with respect to smaller t
• red 9-(28,14,5076) ($\ge 1.6\times 10^{16}$ isomorphism types)

# 17854: 9-(28,14,5076)

• clan: 13-(32,16,423), 2 times derived, 2 times residual
• Alltop construction for design 8-(27,13,5076) (# 17850)

# 17855: 7-(27,13,21840)

• clan: 13-(32,16,546), 1 times reduced t, 3 times derived, 2 times residual
• supplementary design of 8-(27,13,5076) (# 17850) with respect to smaller t
• derived from supplementary of 8-(28,14,16920) (# 17853)
• Tran van Trung construction (right) for 7-(26,12,6552) (# 17856) : der= 7-(26,12,6552) and res= 7-(26,13,15288) - the given design is the derived.
• Tran van Trung construction (left) for 7-(26,13,15288) (# 17857) : der= 7-(26,12,6552) and res= 7-(26,13,15288) - the given design is the residual.
• derived from 8-(28,14,21840) (# 17867)
• design 8-(27,13,6552) (# 17868) with respect to smaller t

# 17856: 7-(26,12,6552)

• clan: 13-(32,16,546), 4 times derived, 2 times residual
• derived from supplementary of 8-(27,13,5076) (# 17850)
• derived from 8-(27,13,6552) (# 17868)

# 17857: 7-(26,13,15288)

• clan: 13-(32,16,546), 3 times derived, 3 times residual
• residual design of supplementary of 8-(27,13,5076) (# 17850)
• Alltop construction for design 6-(25,12,15288) (# 17861)
• derived from supplementary of 8-(27,14,11844) (# 17866)
• residual design of 8-(27,13,6552) (# 17868)
• derived from 8-(27,14,15288) (# 17869)

# 17858: 6-(25,11,5076)

• clan: 13-(32,16,423), 5 times derived, 2 times residual
• derived from 7-(26,12,5076) (# 17851)
• derived from supplementary of 7-(26,12,6552) (# 17856)

# 17859: 6-(25,12,11844)

• clan: 13-(32,16,423), 4 times derived, 3 times residual
• residual design of 7-(26,12,5076) (# 17851)
• derived from 7-(26,13,11844) (# 17852)
• residual design of supplementary of 7-(26,12,6552) (# 17856)
• derived from supplementary of 7-(26,13,15288) (# 17857)

# 17860: 6-(25,11,6552)

• clan: 13-(32,16,546), 5 times derived, 2 times residual
• derived from supplementary of 7-(26,12,5076) (# 17851)
• derived from 7-(26,12,6552) (# 17856)

# 17861: 6-(25,12,15288)

• clan: 13-(32,16,546), 4 times derived, 3 times residual
• residual design of supplementary of 7-(26,12,5076) (# 17851)
• derived from supplementary of 7-(26,13,11844) (# 17852)
• residual design of 7-(26,12,6552) (# 17856)
• derived from 7-(26,13,15288) (# 17857)

# 17862: 6-(25,13,21996)

• clan: 13-(32,16,423), 3 times derived, 4 times residual
• residual design of 7-(26,13,11844) (# 17852)
• residual design of supplementary of 7-(26,13,15288) (# 17857)
• derived from 7-(26,14,21996) (# 17878)
• derived from supplementary of 7-(26,14,28392) (# 17879)

# 17863: 6-(25,13,28392)

• clan: 13-(32,16,546), 3 times derived, 4 times residual
• residual design of supplementary of 7-(26,13,11844) (# 17852)
• residual design of 7-(26,13,15288) (# 17857)
• derived from supplementary of 7-(26,14,21996) (# 17878)
• derived from 7-(26,14,28392) (# 17879)

# 17864: 7-(27,14,33840)

• clan: 13-(32,16,423), 1 times reduced t, 2 times derived, 3 times residual
• residual design of 8-(28,14,16920) (# 17853)
• design 8-(27,14,11844) (# 17866) with respect to smaller t
• residual design of supplementary of 8-(28,14,21840) (# 17867)
• supplementary design of 8-(27,14,15288) (# 17869) with respect to smaller t
• Tran van Trung construction (left) for 7-(26,14,21996) (# 17878) : der= 7-(26,13,11844) and res= 7-(26,14,21996) - the given design is the residual.

# 17865: 7-(27,14,43680)

• clan: 13-(32,16,546), 1 times reduced t, 2 times derived, 3 times residual
• residual design of supplementary of 8-(28,14,16920) (# 17853)
• supplementary design of 8-(27,14,11844) (# 17866) with respect to smaller t
• residual design of 8-(28,14,21840) (# 17867)
• design 8-(27,14,15288) (# 17869) with respect to smaller t
• Tran van Trung construction (left) for 7-(26,14,28392) (# 17879) : der= 7-(26,13,15288) and res= 7-(26,14,28392) - the given design is the residual.

# 17866: 8-(27,14,11844)

• clan: 13-(32,16,423), 2 times derived, 3 times residual
• residual design of 9-(28,14,5076) (# 17854)
• residual design of supplementary of 9-(28,14,6552) (# 17880)

# 17867: 8-(28,14,21840)

• clan: 13-(32,16,546), 1 times reduced t, 2 times derived, 2 times residual
• supplementary design of 9-(28,14,5076) (# 17854) with respect to smaller t
• Tran van Trung construction with complementary design for 8-(27,13,6552) (# 17868)
• Tran van Trung construction (right) for 8-(27,13,6552) (# 17868) : der= 8-(27,13,6552) and res= 8-(27,14,15288) - the given design is the derived.
• Tran van Trung construction (left) for 8-(27,14,15288) (# 17869) : der= 8-(27,13,6552) and res= 8-(27,14,15288) - the given design is the residual.
• design 9-(28,14,6552) (# 17880) with respect to smaller t

# 17868: 8-(27,13,6552)

• clan: 13-(32,16,546), 3 times derived, 2 times residual
• derived from supplementary of 9-(28,14,5076) (# 17854)
• derived from 9-(28,14,6552) (# 17880)

# 17869: 8-(27,14,15288)

• clan: 13-(32,16,546), 2 times derived, 3 times residual
• residual design of supplementary of 9-(28,14,5076) (# 17854)
• residual design of 9-(28,14,6552) (# 17880)

# 17870: 5-(24,11,11844)

• clan: 13-(32,16,423), 5 times derived, 3 times residual
• residual design of 6-(25,11,5076) (# 17858)
• derived from 6-(25,12,11844) (# 17859)
• residual design of supplementary of 6-(25,11,6552) (# 17860)
• derived from supplementary of 6-(25,12,15288) (# 17861)

# 17871: 5-(24,10,6552)

• clan: 13-(32,16,546), 6 times derived, 2 times residual
• derived from supplementary of 6-(25,11,5076) (# 17858)
• derived from 6-(25,11,6552) (# 17860)

# 17872: 5-(24,11,15288)

• clan: 13-(32,16,546), 5 times derived, 3 times residual
• residual design of supplementary of 6-(25,11,5076) (# 17858)
• derived from supplementary of 6-(25,12,11844) (# 17859)
• residual design of 6-(25,11,6552) (# 17860)
• derived from 6-(25,12,15288) (# 17861)

# 17873: 5-(24,12,28392)

• clan: 13-(32,16,546), 4 times derived, 4 times residual
• residual design of supplementary of 6-(25,12,11844) (# 17859)
• residual design of 6-(25,12,15288) (# 17861)
• derived from supplementary of 6-(25,13,21996) (# 17862)
• derived from 6-(25,13,28392) (# 17863)

# 17874: 5-(24,13,32994)

• clan: 13-(32,16,423), 3 times derived, 5 times residual
• residual design of 6-(25,13,21996) (# 17862)
• residual design of supplementary of 6-(25,13,28392) (# 17863)
• derived from 6-(25,14,32994) (# 17883)
• derived from supplementary of 6-(25,14,42588) (# 17884)

# 17875: 5-(24,13,42588)

• clan: 13-(32,16,546), 3 times derived, 5 times residual
• residual design of supplementary of 6-(25,13,21996) (# 17862)
• residual design of 6-(25,13,28392) (# 17863)
• derived from supplementary of 6-(25,14,32994) (# 17883)
• derived from 6-(25,14,42588) (# 17884)

# 17876: 6-(26,14,54990)

• clan: 13-(32,16,423), 1 times reduced t, 2 times derived, 4 times residual
• residual design of 7-(27,14,33840) (# 17864)
• residual design of supplementary of 7-(27,14,43680) (# 17865)
• design 7-(26,14,21996) (# 17878) with respect to smaller t
• supplementary design of 7-(26,14,28392) (# 17879) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,14,32994) (# 17883) : der= 6-(25,13,21996) and res= 6-(25,14,32994) - the given design is the residual.

# 17877: 6-(26,14,70980)

• clan: 13-(32,16,546), 1 times reduced t, 2 times derived, 4 times residual
• residual design of supplementary of 7-(27,14,33840) (# 17864)
• residual design of 7-(27,14,43680) (# 17865)
• supplementary design of 7-(26,14,21996) (# 17878) with respect to smaller t
• design 7-(26,14,28392) (# 17879) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,14,42588) (# 17884) : der= 6-(25,13,28392) and res= 6-(25,14,42588) - the given design is the residual.

# 17878: 7-(26,14,21996)

• clan: 13-(32,16,423), 2 times derived, 4 times residual
• residual design of 8-(27,14,11844) (# 17866)
• residual design of supplementary of 8-(27,14,15288) (# 17869)

# 17879: 7-(26,14,28392)

• clan: 13-(32,16,546), 2 times derived, 4 times residual
• residual design of supplementary of 8-(27,14,11844) (# 17866)
• residual design of 8-(27,14,15288) (# 17869)

# 17880: 9-(28,14,6552)

• clan: 13-(32,16,546), 2 times derived, 2 times residual
• Alltop construction for design 8-(27,13,6552) (# 17868)

# 17881: 5-(25,14,73320)

• clan: 13-(32,16,423), 1 times reduced t, 2 times derived, 5 times residual
• residual design of 6-(26,14,54990) (# 17876)
• residual design of supplementary of 6-(26,14,70980) (# 17877)
• design 6-(25,14,32994) (# 17883) with respect to smaller t
• supplementary design of 6-(25,14,42588) (# 17884) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,14,40326) (# 17885) : der= 5-(24,13,32994) and res= 5-(24,14,40326) - the given design is the residual.

# 17882: 5-(25,14,94640)

• clan: 13-(32,16,546), 1 times reduced t, 2 times derived, 5 times residual
• residual design of supplementary of 6-(26,14,54990) (# 17876)
• residual design of 6-(26,14,70980) (# 17877)
• supplementary design of 6-(25,14,32994) (# 17883) with respect to smaller t
• design 6-(25,14,42588) (# 17884) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,14,52052) (# 17886) : der= 5-(24,13,42588) and res= 5-(24,14,52052) - the given design is the residual.

# 17883: 6-(25,14,32994)

• clan: 13-(32,16,423), 2 times derived, 5 times residual
• residual design of 7-(26,14,21996) (# 17878)
• residual design of supplementary of 7-(26,14,28392) (# 17879)

# 17884: 6-(25,14,42588)

• clan: 13-(32,16,546), 2 times derived, 5 times residual
• residual design of supplementary of 7-(26,14,21996) (# 17878)
• residual design of 7-(26,14,28392) (# 17879)

# 17885: 5-(24,14,40326)

• clan: 13-(32,16,423), 2 times derived, 6 times residual
• residual design of 6-(25,14,32994) (# 17883)
• residual design of supplementary of 6-(25,14,42588) (# 17884)

# 17886: 5-(24,14,52052)

• clan: 13-(32,16,546), 2 times derived, 6 times residual
• residual design of supplementary of 6-(25,14,32994) (# 17883)
• residual design of 6-(25,14,42588) (# 17884)

# 17887: 8-(27,13,5148)

• clan: 13-(32,16,429), 3 times derived, 2 times residual
• $ASL(3,3)$
• derived from 9-(28,14,5148) (# 17890)
• derived from supplementary of 9-(28,14,6480) (# 17905)

# 17888: 7-(26,12,5148)

• clan: 13-(32,16,429), 4 times derived, 2 times residual
• derived from 8-(27,13,5148) (# 17887)
• derived from supplementary of 8-(27,13,6480) (# 17898)

# 17889: 8-(28,14,17160)

• clan: 13-(32,16,429), 1 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 8-(27,13,5148) (# 17887)
• design 9-(28,14,5148) (# 17890) with respect to smaller t
• Tran van Trung construction (left) for 8-(27,14,12012) (# 17896) : der= 8-(27,13,5148) and res= 8-(27,14,12012) - the given design is the residual.
• supplementary design of 9-(28,14,6480) (# 17905) with respect to smaller t
• red 9-(28,14,5148) ($\ge 1.6\times 10^{16}$ isomorphism types)

# 17890: 9-(28,14,5148)

• clan: 13-(32,16,429), 2 times derived, 2 times residual
• Alltop construction for design 8-(27,13,5148) (# 17887)

# 17891: 7-(27,13,21600)

• clan: 13-(32,16,540), 1 times reduced t, 3 times derived, 2 times residual
• supplementary design of 8-(27,13,5148) (# 17887) with respect to smaller t
• derived from supplementary of 8-(28,14,17160) (# 17889)
• Tran van Trung construction (right) for 7-(26,12,6480) (# 17892) : der= 7-(26,12,6480) and res= 7-(26,13,15120) - the given design is the derived.
• derived from 8-(28,14,21600) (# 17897)
• design 8-(27,13,6480) (# 17898) with respect to smaller t

# 17892: 7-(26,12,6480)

• clan: 13-(32,16,540), 4 times derived, 2 times residual
• derived from supplementary of 8-(27,13,5148) (# 17887)
• derived from 8-(27,13,6480) (# 17898)

# 17893: 7-(27,12,6864)

• clan: 13-(32,16,429), 1 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (left) for 7-(26,12,5148) (# 17888) : der= 7-(26,11,1716) and res= 7-(26,12,5148) - the given design is the residual.

# 17894: 7-(27,14,34320)

• clan: 13-(32,16,429), 1 times reduced t, 2 times derived, 3 times residual
• residual design of 8-(28,14,17160) (# 17889)
• design 8-(27,14,12012) (# 17896) with respect to smaller t
• residual design of supplementary of 8-(28,14,21600) (# 17897)
• supplementary design of 8-(27,14,15120) (# 17899) with respect to smaller t
• Tran van Trung construction (left) for 7-(26,14,22308) (# 17903) : der= 7-(26,13,12012) and res= 7-(26,14,22308) - the given design is the residual.

# 17895: 7-(27,14,43200)

• clan: 13-(32,16,540), 1 times reduced t, 2 times derived, 3 times residual
• residual design of supplementary of 8-(28,14,17160) (# 17889)
• supplementary design of 8-(27,14,12012) (# 17896) with respect to smaller t
• residual design of 8-(28,14,21600) (# 17897)
• design 8-(27,14,15120) (# 17899) with respect to smaller t
• Tran van Trung construction (left) for 7-(26,14,28080) (# 17904) : der= 7-(26,13,15120) and res= 7-(26,14,28080) - the given design is the residual.

# 17896: 8-(27,14,12012)

• clan: 13-(32,16,429), 2 times derived, 3 times residual
• residual design of 9-(28,14,5148) (# 17890)
• residual design of supplementary of 9-(28,14,6480) (# 17905)

# 17897: 8-(28,14,21600)

• clan: 13-(32,16,540), 1 times reduced t, 2 times derived, 2 times residual
• supplementary design of 9-(28,14,5148) (# 17890) with respect to smaller t
• Tran van Trung construction with complementary design for 8-(27,13,6480) (# 17898)
• Tran van Trung construction (right) for 8-(27,13,6480) (# 17898) : der= 8-(27,13,6480) and res= 8-(27,14,15120) - the given design is the derived.
• Tran van Trung construction (left) for 8-(27,14,15120) (# 17899) : der= 8-(27,13,6480) and res= 8-(27,14,15120) - the given design is the residual.
• design 9-(28,14,6480) (# 17905) with respect to smaller t

# 17898: 8-(27,13,6480)

• clan: 13-(32,16,540), 3 times derived, 2 times residual
• derived from supplementary of 9-(28,14,5148) (# 17890)
• derived from 9-(28,14,6480) (# 17905)

# 17899: 8-(27,14,15120)

• clan: 13-(32,16,540), 2 times derived, 3 times residual
• residual design of supplementary of 9-(28,14,5148) (# 17890)
• residual design of 9-(28,14,6480) (# 17905)

created: Fri Oct 23 11:14:45 CEST 2009