t designs with small t, id ge 13400

• clan: 15-(32,16,9), 4 times reduced t, 5 times derived
• Tran van Trung construction (right) for 6-(26,10,2565) (# 13397) : der= 6-(26,10,2565) and res= 6-(26,11,8208) - the given design is the derived.
• Tran van Trung construction (left) for 6-(26,11,8208) (# 13398) : der= 6-(26,10,2565) and res= 6-(26,11,8208) - the given design is the residual.
• supplementary design of 7-(27,11,2280) (# 14307) with respect to smaller t

# 13401: 6-(27,12,28728)

• clan: 15-(32,16,9), 4 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(26,11,8208) (# 13398) : der= 6-(26,11,8208) and res= 6-(26,12,20520) - the given design is the derived.

# 13402: 6-(28,12,35112)

• clan: 15-(32,16,8), 5 times reduced t, 4 times derived
• Tran van Trung construction (left) for 6-(27,12,25536) (# 13399) : der= 6-(27,11,9576) and res= 6-(27,12,25536) - the given design is the residual.

# 13403: 6-(28,13,80256)

• clan: 15-(32,16,8), 5 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(27,12,25536) (# 13399) : der= 6-(27,12,25536) and res= 6-(27,13,54720) - the given design is the derived.

# 13404: 6-(28,12,39501)

• clan: 15-(32,16,9), 5 times reduced t, 4 times derived
• Tran van Trung construction (right) for 6-(27,11,10773) (# 13400) : der= 6-(27,11,10773) and res= 6-(27,12,28728) - the given design is the derived.
• Tran van Trung construction (left) for 6-(27,12,28728) (# 13401) : der= 6-(27,11,10773) and res= 6-(27,12,28728) - the given design is the residual.

# 13405: 6-(28,13,90288)

• clan: 15-(32,16,9), 5 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(27,12,28728) (# 13401) : der= 6-(27,12,28728) and res= 6-(27,13,61560) - the given design is the derived.

# 13406: 6-(29,13,115368)

• clan: 15-(32,16,8), 6 times reduced t, 3 times derived
• Tran van Trung construction (right) for 6-(28,12,35112) (# 13402) : der= 6-(28,12,35112) and res= 6-(28,13,80256) - the given design is the derived.
• Tran van Trung construction (left) for 6-(28,13,80256) (# 13403) : der= 6-(28,12,35112) and res= 6-(28,13,80256) - the given design is the residual.

# 13407: 6-(29,14,230736)

• clan: 15-(32,16,8), 6 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(28,13,80256) (# 13403) : der= 6-(28,13,80256) and res= 6-(28,14,150480) - the given design is the derived.
• derived from 7-(30,15,230736) (# 13412)
• derived from supplementary of 7-(30,15,259578) (# 13415)

# 13408: 6-(29,13,129789)

• clan: 15-(32,16,9), 6 times reduced t, 3 times derived
• Tran van Trung construction (right) for 6-(28,12,39501) (# 13404) : der= 6-(28,12,39501) and res= 6-(28,13,90288) - the given design is the derived.
• Tran van Trung construction (left) for 6-(28,13,90288) (# 13405) : der= 6-(28,12,39501) and res= 6-(28,13,90288) - the given design is the residual.

# 13409: 6-(29,14,259578)

• clan: 15-(32,16,9), 6 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(28,13,90288) (# 13405) : der= 6-(28,13,90288) and res= 6-(28,14,169290) - the given design is the derived.
• derived from supplementary of 7-(30,15,230736) (# 13412)
• derived from 7-(30,15,259578) (# 13415)

# 13410: 6-(30,14,346104)

• clan: 15-(32,16,8), 7 times reduced t, 2 times derived
• Tran van Trung construction (right) for 6-(29,13,115368) (# 13406) : der= 6-(29,13,115368) and res= 6-(29,14,230736) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,14,230736) (# 13407) : der= 6-(29,13,115368) and res= 6-(29,14,230736) - the given design is the residual.

# 13411: 6-(30,15,615296)

• clan: 15-(32,16,8), 7 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 6-(29,14,230736) (# 13407)
• design 7-(30,15,230736) (# 13412) with respect to smaller t
• supplementary design of 7-(30,15,259578) (# 13415) with respect to smaller t
• Tran van Trung construction (left) for 6-(29,15,384560) (# 13419) : der= 6-(29,14,230736) and res= 6-(29,15,384560) - the given design is the residual.

# 13412: 7-(30,15,230736)

• clan: 15-(32,16,8), 6 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(29,14,230736) (# 13407)

# 13413: 6-(30,14,389367)

• clan: 15-(32,16,9), 7 times reduced t, 2 times derived
• Tran van Trung construction (right) for 6-(29,13,129789) (# 13408) : der= 6-(29,13,129789) and res= 6-(29,14,259578) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,14,259578) (# 13409) : der= 6-(29,13,129789) and res= 6-(29,14,259578) - the given design is the residual.

# 13414: 6-(30,15,692208)

• clan: 15-(32,16,9), 7 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 6-(29,14,259578) (# 13409)
• supplementary design of 7-(30,15,230736) (# 13412) with respect to smaller t
• design 7-(30,15,259578) (# 13415) with respect to smaller t
• Tran van Trung construction (left) for 6-(29,15,432630) (# 13420) : der= 6-(29,14,259578) and res= 6-(29,15,432630) - the given design is the residual.

# 13415: 7-(30,15,259578)

• clan: 15-(32,16,9), 6 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(29,14,259578) (# 13409)

# 13416: 6-(31,15,961400)

• clan: 15-(32,16,8), 8 times reduced t, 1 times derived
• Tran van Trung construction (right) for 6-(30,14,346104) (# 13410) : der= 6-(30,14,346104) and res= 6-(30,15,615296) - the given design is the derived.
• Tran van Trung construction (left) for 6-(30,15,615296) (# 13411) : der= 6-(30,14,346104) and res= 6-(30,15,615296) - the given design is the residual.
• derived from 7-(32,16,961400) (# 13423)
• derived from supplementary of 7-(32,16,1081575) (# 13427)

# 13417: 5-(29,15,922944)

• clan: 15-(32,16,8), 7 times reduced t, 1 times derived, 2 times residual
• residual design of 6-(30,15,615296) (# 13411)
• residual design of supplementary of 6-(30,15,692208) (# 13414)
• design 6-(29,15,384560) (# 13419) with respect to smaller t
• supplementary design of 6-(29,15,432630) (# 13420) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,15,538384) (# 13424) : der= 5-(28,14,384560) and res= 5-(28,15,538384) - the given design is the residual.

# 13418: 5-(29,15,1038312)

• clan: 15-(32,16,9), 7 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 6-(30,15,615296) (# 13411)
• residual design of 6-(30,15,692208) (# 13414)
• supplementary design of 6-(29,15,384560) (# 13419) with respect to smaller t
• design 6-(29,15,432630) (# 13420) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,15,605682) (# 13425) : der= 5-(28,14,432630) and res= 5-(28,15,605682) - the given design is the residual.

# 13419: 6-(29,15,384560)

• clan: 15-(32,16,8), 6 times reduced t, 1 times derived, 2 times residual
• residual design of 7-(30,15,230736) (# 13412)
• residual design of supplementary of 7-(30,15,259578) (# 13415)

# 13420: 6-(29,15,432630)

• clan: 15-(32,16,9), 6 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 7-(30,15,230736) (# 13412)
• residual design of 7-(30,15,259578) (# 13415)

# 13421: 6-(31,15,1081575)

• clan: 15-(32,16,9), 8 times reduced t, 1 times derived
• Tran van Trung construction (right) for 6-(30,14,389367) (# 13413) : der= 6-(30,14,389367) and res= 6-(30,15,692208) - the given design is the derived.
• Tran van Trung construction (left) for 6-(30,15,692208) (# 13414) : der= 6-(30,14,389367) and res= 6-(30,15,692208) - the given design is the residual.
• derived from supplementary of 7-(32,16,961400) (# 13423)
• derived from 7-(32,16,1081575) (# 13427)

# 13422: 6-(32,16,2499640)

• clan: 15-(32,16,8), 9 times reduced t
• Tran van Trung construction with complementary design for 6-(31,15,961400) (# 13416)
• design 7-(32,16,961400) (# 13423) with respect to smaller t
• supplementary design of 7-(32,16,1081575) (# 13427) with respect to smaller t
• Tran van Trung construction (left) for 6-(31,16,1538240) (# 13430) : der= 6-(31,15,961400) and res= 6-(31,16,1538240) - the given design is the residual.

# 13423: 7-(32,16,961400)

• clan: 15-(32,16,8), 8 times reduced t
• Alltop construction for design 6-(31,15,961400) (# 13416)

# 13424: 5-(28,15,538384)

• clan: 15-(32,16,8), 6 times reduced t, 1 times derived, 3 times residual
• residual design of 6-(29,15,384560) (# 13419)
• residual design of supplementary of 6-(29,15,432630) (# 13420)

# 13425: 5-(28,15,605682)

• clan: 15-(32,16,9), 6 times reduced t, 1 times derived, 3 times residual
• residual design of supplementary of 6-(29,15,384560) (# 13419)
• residual design of 6-(29,15,432630) (# 13420)

# 13426: 6-(32,16,2812095)

• clan: 15-(32,16,9), 9 times reduced t
• Tran van Trung construction with complementary design for 6-(31,15,1081575) (# 13421)
• supplementary design of 7-(32,16,961400) (# 13423) with respect to smaller t
• design 7-(32,16,1081575) (# 13427) with respect to smaller t
• Tran van Trung construction (left) for 6-(31,16,1730520) (# 13431) : der= 6-(31,15,1081575) and res= 6-(31,16,1730520) - the given design is the residual.

# 13427: 7-(32,16,1081575)

• clan: 15-(32,16,9), 8 times reduced t
• Alltop construction for design 6-(31,15,1081575) (# 13421)

# 13428: 5-(31,16,3635840)

• clan: 15-(32,16,8), 9 times reduced t, 1 times residual
• residual design of 6-(32,16,2499640) (# 13422)
• residual design of supplementary of 6-(32,16,2812095) (# 13426)
• design 6-(31,16,1538240) (# 13430) with respect to smaller t
• supplementary design of 6-(31,16,1730520) (# 13431) with respect to smaller t
• Tran van Trung construction (left) for 5-(30,16,2097600) (# 13432) : der= 5-(30,15,1538240) and res= 5-(30,16,2097600) - the given design is the residual.

# 13429: 5-(31,16,4090320)

• clan: 15-(32,16,9), 9 times reduced t, 1 times residual
• residual design of supplementary of 6-(32,16,2499640) (# 13422)
• residual design of 6-(32,16,2812095) (# 13426)
• supplementary design of 6-(31,16,1538240) (# 13430) with respect to smaller t
• design 6-(31,16,1730520) (# 13431) with respect to smaller t
• Tran van Trung construction (left) for 5-(30,16,2359800) (# 13433) : der= 5-(30,15,1730520) and res= 5-(30,16,2359800) - the given design is the residual.

# 13430: 6-(31,16,1538240)

• clan: 15-(32,16,8), 8 times reduced t, 1 times residual
• residual design of 7-(32,16,961400) (# 13423)
• residual design of supplementary of 7-(32,16,1081575) (# 13427)

# 13431: 6-(31,16,1730520)

• clan: 15-(32,16,9), 8 times reduced t, 1 times residual
• residual design of supplementary of 7-(32,16,961400) (# 13423)
• residual design of 7-(32,16,1081575) (# 13427)

# 13432: 5-(30,16,2097600)

• clan: 15-(32,16,8), 8 times reduced t, 2 times residual
• residual design of 6-(31,16,1538240) (# 13430)
• residual design of supplementary of 6-(31,16,1730520) (# 13431)

# 13433: 5-(30,16,2359800)

• clan: 15-(32,16,9), 8 times reduced t, 2 times residual
• residual design of supplementary of 6-(31,16,1538240) (# 13430)
• residual design of 6-(31,16,1730520) (# 13431)

# 13434: 7-(24,9,40)

• clan: 15-(32,16,5), 7 times derived, 1 times residual
• PGL(2,23) (113 isom. types) \cite{Bettenetal98b}

# 13435: 6-(24,9,240)

• clan: 15-(32,16,5), 1 times reduced t, 7 times derived, 1 times residual
• design 7-(24,9,40) (# 13434) with respect to smaller t
• Tran van Trung construction (left) for 6-(23,9,200) (# 13436) : der= 6-(23,8,40) and res= 6-(23,9,200) - the given design is the residual.
• residual design of 7-(25,9,45) (# 13439)

# 13436: 6-(23,9,200)

• clan: 15-(32,16,5), 7 times derived, 2 times residual
• residual design of 7-(24,9,40) (# 13434)

# 13437: 6-(24,9,576)

• clan: 15-(32,16,12), 1 times reduced t, 7 times derived, 1 times residual
• supplementary design of 7-(24,9,40) (# 13434) with respect to smaller t
• Tran van Trung construction (left) for 6-(23,9,480) (# 13438) : der= 6-(23,8,96) and res= 6-(23,9,480) - the given design is the residual.
• residual design of supplementary of 7-(25,9,45) (# 13439)

# 13438: 6-(23,9,480)

• clan: 15-(32,16,12), 7 times derived, 2 times residual
• residual design of supplementary of 7-(24,9,40) (# 13434)

# 13439: 7-(25,9,45)

• clan: 15-(32,16,5), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 7-(24,9,40) (# 13434) : der= 7-(24,8,5) and res= 7-(24,9,40) - the given design is the residual.
• (Tran van Trung construction): 7-(24,8,5) together with 7-(24,9,40) \cite{Bettenetal98b} 131210855332052182104 isomorphism types

# 13440: 6-(24,10,900)

• clan: 15-(32,16,5), 1 times reduced t, 6 times derived, 2 times residual
• Tran van Trung construction (right) for 6-(23,9,200) (# 13436) : der= 6-(23,9,200) and res= 6-(23,10,700) - the given design is the derived.

# 13441: 6-(25,9,684)

• clan: 15-(32,16,12), 2 times reduced t, 7 times derived
• Tran van Trung construction (left) for 6-(24,9,576) (# 13437) : der= 6-(24,8,108) and res= 6-(24,9,576) - the given design is the residual.
• supplementary design of 7-(25,9,45) (# 13439) with respect to smaller t

# 13442: 6-(25,10,1140)

• clan: 15-(32,16,5), 2 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (left) for 6-(24,10,900) (# 13440) : der= 6-(24,9,240) and res= 6-(24,10,900) - the given design is the residual.

# 13443: 6-(25,11,3420)

• clan: 15-(32,16,5), 2 times reduced t, 5 times derived, 2 times residual
• Tran van Trung construction (right) for 6-(24,10,900) (# 13440) : der= 6-(24,10,900) and res= 6-(24,11,2520) - the given design is the derived.

# 13444: 6-(26,11,4560)

• clan: 15-(32,16,5), 3 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(25,10,1140) (# 13442) : der= 6-(25,10,1140) and res= 6-(25,11,3420) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,11,3420) (# 13443) : der= 6-(25,10,1140) and res= 6-(25,11,3420) - the given design is the residual.

# 13445: 6-(26,12,11400)

• clan: 15-(32,16,5), 3 times reduced t, 4 times derived, 2 times residual
• Tran van Trung construction (right) for 6-(25,11,3420) (# 13443) : der= 6-(25,11,3420) and res= 6-(25,12,7980) - the given design is the derived.

# 13446: 6-(27,11,5985)

• clan: 15-(32,16,5), 4 times reduced t, 5 times derived
• Tran van Trung construction (left) for 6-(26,11,4560) (# 13444) : der= 6-(26,10,1425) and res= 6-(26,11,4560) - the given design is the residual.

# 13447: 6-(27,12,15960)

• clan: 15-(32,16,5), 4 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(26,11,4560) (# 13444) : der= 6-(26,11,4560) and res= 6-(26,12,11400) - the given design is the derived.
• Tran van Trung construction (left) for 6-(26,12,11400) (# 13445) : der= 6-(26,11,4560) and res= 6-(26,12,11400) - the given design is the residual.

# 13448: 6-(27,13,34200)

• clan: 15-(32,16,5), 4 times reduced t, 3 times derived, 2 times residual
• Tran van Trung construction (right) for 6-(26,12,11400) (# 13445) : der= 6-(26,12,11400) and res= 6-(26,13,22800) - the given design is the derived.
• derived from 7-(28,14,34200) (# 13452)
• derived from supplementary of 7-(28,14,82080) (# 13466)

# 13449: 6-(28,12,21945)

• clan: 15-(32,16,5), 5 times reduced t, 4 times derived
• Tran van Trung construction (right) for 6-(27,11,5985) (# 13446) : der= 6-(27,11,5985) and res= 6-(27,12,15960) - the given design is the derived.
• Tran van Trung construction (left) for 6-(27,12,15960) (# 13447) : der= 6-(27,11,5985) and res= 6-(27,12,15960) - the given design is the residual.

# 13450: 6-(28,13,50160)

• clan: 15-(32,16,5), 5 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(27,12,15960) (# 13447) : der= 6-(27,12,15960) and res= 6-(27,13,34200) - the given design is the derived.
• Tran van Trung construction (left) for 6-(27,13,34200) (# 13448) : der= 6-(27,12,15960) and res= 6-(27,13,34200) - the given design is the residual.

# 13451: 6-(28,14,94050)

• clan: 15-(32,16,5), 5 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 6-(27,13,34200) (# 13448)
• design 7-(28,14,34200) (# 13452) with respect to smaller t
• Tran van Trung construction (left) for 6-(27,14,59850) (# 13457) : der= 6-(27,13,34200) and res= 6-(27,14,59850) - the given design is the residual.
• supplementary design of 7-(28,14,82080) (# 13466) with respect to smaller t

# 13452: 7-(28,14,34200)

• clan: 15-(32,16,5), 4 times reduced t, 2 times derived, 2 times residual
• Alltop construction for design 6-(27,13,34200) (# 13448)

# 13453: 6-(29,13,72105)

• clan: 15-(32,16,5), 6 times reduced t, 3 times derived
• Tran van Trung construction (right) for 6-(28,12,21945) (# 13449) : der= 6-(28,12,21945) and res= 6-(28,13,50160) - the given design is the derived.
• Tran van Trung construction (left) for 6-(28,13,50160) (# 13450) : der= 6-(28,12,21945) and res= 6-(28,13,50160) - the given design is the residual.

# 13454: 6-(29,14,144210)

• clan: 15-(32,16,5), 6 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(28,13,50160) (# 13450) : der= 6-(28,13,50160) and res= 6-(28,14,94050) - the given design is the derived.
• Tran van Trung construction (left) for 6-(28,14,94050) (# 13451) : der= 6-(28,13,50160) and res= 6-(28,14,94050) - the given design is the residual.
• derived from 7-(30,15,144210) (# 13463)
• derived from supplementary of 7-(30,15,346104) (# 13478)

# 13455: 5-(27,14,146300)

• clan: 15-(32,16,5), 5 times reduced t, 2 times derived, 3 times residual
• residual design of 6-(28,14,94050) (# 13451)
• design 6-(27,14,59850) (# 13457) with respect to smaller t
• residual design of supplementary of 6-(28,14,225720) (# 13458)
• supplementary design of 6-(27,14,143640) (# 13460) with respect to smaller t
• Tran van Trung construction (left) for 5-(26,14,86450) (# 13464) : der= 5-(26,13,59850) and res= 5-(26,14,86450) - the given design is the residual.

# 13456: 5-(27,14,351120)

• clan: 15-(32,16,12), 5 times reduced t, 2 times derived, 3 times residual
• residual design of supplementary of 6-(28,14,94050) (# 13451)
• supplementary design of 6-(27,14,59850) (# 13457) with respect to smaller t
• residual design of 6-(28,14,225720) (# 13458)
• design 6-(27,14,143640) (# 13460) with respect to smaller t
• Tran van Trung construction (left) for 5-(26,14,207480) (# 13465) : der= 5-(26,13,143640) and res= 5-(26,14,207480) - the given design is the residual.

# 13457: 6-(27,14,59850)

• clan: 15-(32,16,5), 4 times reduced t, 2 times derived, 3 times residual
• residual design of 7-(28,14,34200) (# 13452)
• residual design of supplementary of 7-(28,14,82080) (# 13466)

# 13458: 6-(28,14,225720)

• clan: 15-(32,16,12), 5 times reduced t, 2 times derived, 2 times residual
• supplementary design of 7-(28,14,34200) (# 13452) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(27,13,82080) (# 13459)
• Tran van Trung construction (right) for 6-(27,13,82080) (# 13459) : der= 6-(27,13,82080) and res= 6-(27,14,143640) - the given design is the derived.
• Tran van Trung construction (left) for 6-(27,14,143640) (# 13460) : der= 6-(27,13,82080) and res= 6-(27,14,143640) - the given design is the residual.
• design 7-(28,14,82080) (# 13466) with respect to smaller t

# 13459: 6-(27,13,82080)

• clan: 15-(32,16,12), 4 times reduced t, 3 times derived, 2 times residual
• derived from supplementary of 7-(28,14,34200) (# 13452)
• derived from 7-(28,14,82080) (# 13466)

# 13460: 6-(27,14,143640)

• clan: 15-(32,16,12), 4 times reduced t, 2 times derived, 3 times residual
• residual design of supplementary of 7-(28,14,34200) (# 13452)
• residual design of 7-(28,14,82080) (# 13466)

# 13461: 6-(30,14,216315)

• clan: 15-(32,16,5), 7 times reduced t, 2 times derived
• Tran van Trung construction (right) for 6-(29,13,72105) (# 13453) : der= 6-(29,13,72105) and res= 6-(29,14,144210) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,14,144210) (# 13454) : der= 6-(29,13,72105) and res= 6-(29,14,144210) - the given design is the residual.

# 13462: 6-(30,15,384560)

• clan: 15-(32,16,5), 7 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 6-(29,14,144210) (# 13454)
• design 7-(30,15,144210) (# 13463) with respect to smaller t
• Tran van Trung construction (left) for 6-(29,15,240350) (# 13470) : der= 6-(29,14,144210) and res= 6-(29,15,240350) - the given design is the residual.
• supplementary design of 7-(30,15,346104) (# 13478) with respect to smaller t

# 13463: 7-(30,15,144210)

• clan: 15-(32,16,5), 6 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(29,14,144210) (# 13454)

# 13464: 5-(26,14,86450)

• clan: 15-(32,16,5), 4 times reduced t, 2 times derived, 4 times residual
• residual design of 6-(27,14,59850) (# 13457)
• residual design of supplementary of 6-(27,14,143640) (# 13460)

# 13465: 5-(26,14,207480)

• clan: 15-(32,16,12), 4 times reduced t, 2 times derived, 4 times residual
• residual design of supplementary of 6-(27,14,59850) (# 13457)
• residual design of 6-(27,14,143640) (# 13460)

# 13466: 7-(28,14,82080)

• clan: 15-(32,16,12), 4 times reduced t, 2 times derived, 2 times residual
• Alltop construction for design 6-(27,13,82080) (# 13459)

# 13467: 6-(31,15,600875)

• clan: 15-(32,16,5), 8 times reduced t, 1 times derived
• Tran van Trung construction (right) for 6-(30,14,216315) (# 13461) : der= 6-(30,14,216315) and res= 6-(30,15,384560) - the given design is the derived.
• Tran van Trung construction (left) for 6-(30,15,384560) (# 13462) : der= 6-(30,14,216315) and res= 6-(30,15,384560) - the given design is the residual.
• derived from 7-(32,16,600875) (# 13475)
• derived from supplementary of 7-(32,16,1442100) (# 13487)

# 13468: 5-(29,15,576840)

• clan: 15-(32,16,5), 7 times reduced t, 1 times derived, 2 times residual
• residual design of 6-(30,15,384560) (# 13462)
• design 6-(29,15,240350) (# 13470) with respect to smaller t
• residual design of supplementary of 6-(30,15,922944) (# 13471)
• supplementary design of 6-(29,15,576840) (# 13473) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,15,336490) (# 13476) : der= 5-(28,14,240350) and res= 5-(28,15,336490) - the given design is the residual.

# 13469: 5-(29,15,1384416)

• clan: 15-(32,16,12), 7 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 6-(30,15,384560) (# 13462)
• supplementary design of 6-(29,15,240350) (# 13470) with respect to smaller t
• residual design of 6-(30,15,922944) (# 13471)
• design 6-(29,15,576840) (# 13473) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,15,807576) (# 13477) : der= 5-(28,14,576840) and res= 5-(28,15,807576) - the given design is the residual.

# 13470: 6-(29,15,240350)

• clan: 15-(32,16,5), 6 times reduced t, 1 times derived, 2 times residual
• residual design of 7-(30,15,144210) (# 13463)
• residual design of supplementary of 7-(30,15,346104) (# 13478)

# 13471: 6-(30,15,922944)

• clan: 15-(32,16,12), 7 times reduced t, 1 times derived, 1 times residual
• supplementary design of 7-(30,15,144210) (# 13463) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(29,14,346104) (# 13472)
• Tran van Trung construction (right) for 6-(29,14,346104) (# 13472) : der= 6-(29,14,346104) and res= 6-(29,15,576840) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,15,576840) (# 13473) : der= 6-(29,14,346104) and res= 6-(29,15,576840) - the given design is the residual.
• design 7-(30,15,346104) (# 13478) with respect to smaller t

# 13472: 6-(29,14,346104)

• clan: 15-(32,16,12), 6 times reduced t, 2 times derived, 1 times residual
• derived from supplementary of 7-(30,15,144210) (# 13463)
• derived from 7-(30,15,346104) (# 13478)

# 13473: 6-(29,15,576840)

• clan: 15-(32,16,12), 6 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 7-(30,15,144210) (# 13463)
• residual design of 7-(30,15,346104) (# 13478)

# 13474: 6-(32,16,1562275)

• clan: 15-(32,16,5), 9 times reduced t
• Tran van Trung construction with complementary design for 6-(31,15,600875) (# 13467)
• design 7-(32,16,600875) (# 13475) with respect to smaller t
• Tran van Trung construction (left) for 6-(31,16,961400) (# 13481) : der= 6-(31,15,600875) and res= 6-(31,16,961400) - the given design is the residual.
• supplementary design of 7-(32,16,1442100) (# 13487) with respect to smaller t

# 13475: 7-(32,16,600875)

• clan: 15-(32,16,5), 8 times reduced t
• Alltop construction for design 6-(31,15,600875) (# 13467)

# 13476: 5-(28,15,336490)

• clan: 15-(32,16,5), 6 times reduced t, 1 times derived, 3 times residual
• residual design of 6-(29,15,240350) (# 13470)
• residual design of supplementary of 6-(29,15,576840) (# 13473)

# 13477: 5-(28,15,807576)

• clan: 15-(32,16,12), 6 times reduced t, 1 times derived, 3 times residual
• residual design of supplementary of 6-(29,15,240350) (# 13470)
• residual design of 6-(29,15,576840) (# 13473)

# 13478: 7-(30,15,346104)

• clan: 15-(32,16,12), 6 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(29,14,346104) (# 13472)

# 13479: 5-(31,16,2272400)

• clan: 15-(32,16,5), 9 times reduced t, 1 times residual
• residual design of 6-(32,16,1562275) (# 13474)
• design 6-(31,16,961400) (# 13481) with respect to smaller t
• residual design of supplementary of 6-(32,16,3749460) (# 13482)
• supplementary design of 6-(31,16,2307360) (# 13484) with respect to smaller t
• Tran van Trung construction (left) for 5-(30,16,1311000) (# 13485) : der= 5-(30,15,961400) and res= 5-(30,16,1311000) - the given design is the residual.

# 13480: 5-(31,16,5453760)

• clan: 15-(32,16,12), 9 times reduced t, 1 times residual
• residual design of supplementary of 6-(32,16,1562275) (# 13474)
• supplementary design of 6-(31,16,961400) (# 13481) with respect to smaller t
• residual design of 6-(32,16,3749460) (# 13482)
• design 6-(31,16,2307360) (# 13484) with respect to smaller t
• Tran van Trung construction (left) for 5-(30,16,3146400) (# 13486) : der= 5-(30,15,2307360) and res= 5-(30,16,3146400) - the given design is the residual.

# 13481: 6-(31,16,961400)

• clan: 15-(32,16,5), 8 times reduced t, 1 times residual
• residual design of 7-(32,16,600875) (# 13475)
• residual design of supplementary of 7-(32,16,1442100) (# 13487)

# 13482: 6-(32,16,3749460)

• clan: 15-(32,16,12), 9 times reduced t
• supplementary design of 7-(32,16,600875) (# 13475) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(31,15,1442100) (# 13483)
• Tran van Trung construction (right) for 6-(31,15,1442100) (# 13483) : der= 6-(31,15,1442100) and res= 6-(31,16,2307360) - the given design is the derived.
• Tran van Trung construction (left) for 6-(31,16,2307360) (# 13484) : der= 6-(31,15,1442100) and res= 6-(31,16,2307360) - the given design is the residual.
• design 7-(32,16,1442100) (# 13487) with respect to smaller t

# 13483: 6-(31,15,1442100)

• clan: 15-(32,16,12), 8 times reduced t, 1 times derived
• derived from supplementary of 7-(32,16,600875) (# 13475)
• derived from 7-(32,16,1442100) (# 13487)

# 13484: 6-(31,16,2307360)

• clan: 15-(32,16,12), 8 times reduced t, 1 times residual
• residual design of supplementary of 7-(32,16,600875) (# 13475)
• residual design of 7-(32,16,1442100) (# 13487)

# 13485: 5-(30,16,1311000)

• clan: 15-(32,16,5), 8 times reduced t, 2 times residual
• residual design of 6-(31,16,961400) (# 13481)
• residual design of supplementary of 6-(31,16,2307360) (# 13484)

# 13486: 5-(30,16,3146400)

• clan: 15-(32,16,12), 8 times reduced t, 2 times residual
• residual design of supplementary of 6-(31,16,961400) (# 13481)
• residual design of 6-(31,16,2307360) (# 13484)

# 13487: 7-(32,16,1442100)

• clan: 15-(32,16,12), 8 times reduced t
• Alltop construction for design 6-(31,15,1442100) (# 13483)

# 13488: 7-(24,9,48)

• clan: 15-(32,16,6), 7 times derived, 1 times residual
• PGL(2,23) (>= 2827 isom. types) \cite{Bettenetal98b}

# 13489: 7-(25,9,54)

• clan: 15-(32,16,6), 1 times reduced t, 7 times derived
• Tran van Trung construction (left) for 7-(24,9,48) (# 13488) : der= 7-(24,8,6) and res= 7-(24,9,48) - the given design is the residual.
• (Tran van Trung construction): 7-(24,8,6) together with 7-(24,9,48) \cite{Bettenetal98b} (>= 11106724087393318560 isomorphism types with trivial automorphism group, >= 125594891886632282241 isomorphism types )

# 13490: 7-(25,10,288)

• clan: 15-(32,16,6), 1 times reduced t, 6 times derived, 1 times residual
• Tran van Trung construction (right) for 7-(24,9,48) (# 13488) : der= 7-(24,9,48) and res= 7-(24,10,240) - the given design is the derived.
• (Tran van Trung construction): 7-(24,9,48) together with 7-(24,10,240) \cite{Bettenetal97b} (>=23786900753834023916 isomorphism types with trivial automorphism group, >=23786911342165204970 isomorphism types )

# 13491: 7-(26,10,342)

• clan: 15-(32,16,6), 2 times reduced t, 6 times derived
• Tran van Trung construction (right) for 7-(25,9,54) (# 13489) : der= 7-(25,9,54) and res= 7-(25,10,288) - the given design is the derived.
• Tran van Trung construction (left) for 7-(25,10,288) (# 13490) : der= 7-(25,9,54) and res= 7-(25,10,288) - the given design is the residual.
• (Tran van Trung construction): 7-(25,9,54) together with 7-(25,10,288) \cite{Bettenetal97b} (>= 157614502214244520820513272599085230602732718703918448640000000 isomorphism types)

# 13492: 7-(26,11,1368)

• clan: 15-(32,16,6), 2 times reduced t, 5 times derived, 1 times residual
• Tran van Trung construction (right) for 7-(25,10,288) (# 13490) : der= 7-(25,10,288) and res= 7-(25,11,1080) - the given design is the derived.

# 13493: 7-(27,11,1710)

• clan: 15-(32,16,6), 3 times reduced t, 5 times derived
• Tran van Trung construction (right) for 7-(26,10,342) (# 13491) : der= 7-(26,10,342) and res= 7-(26,11,1368) - the given design is the derived.
• Tran van Trung construction (left) for 7-(26,11,1368) (# 13492) : der= 7-(26,10,342) and res= 7-(26,11,1368) - the given design is the residual.
• \cite{Sebille98} $AGL(3,3)$

# 13494: 7-(27,12,5472)

• clan: 15-(32,16,6), 3 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (right) for 7-(26,11,1368) (# 13492) : der= 7-(26,11,1368) and res= 7-(26,12,4104) - the given design is the derived.

# 13495: 7-(28,12,7182)

• clan: 15-(32,16,6), 4 times reduced t, 4 times derived
• Tran van Trung construction (right) for 7-(27,11,1710) (# 13493) : der= 7-(27,11,1710) and res= 7-(27,12,5472) - the given design is the derived.
• Tran van Trung construction (left) for 7-(27,12,5472) (# 13494) : der= 7-(27,11,1710) and res= 7-(27,12,5472) - the given design is the residual.

# 13496: 7-(28,13,19152)

• clan: 15-(32,16,6), 4 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 7-(27,12,5472) (# 13494) : der= 7-(27,12,5472) and res= 7-(27,13,13680) - the given design is the derived.

# 13497: 7-(29,13,26334)

• clan: 15-(32,16,6), 5 times reduced t, 3 times derived
• Tran van Trung construction (right) for 7-(28,12,7182) (# 13495) : der= 7-(28,12,7182) and res= 7-(28,13,19152) - the given design is the derived.
• Tran van Trung construction (left) for 7-(28,13,19152) (# 13496) : der= 7-(28,12,7182) and res= 7-(28,13,19152) - the given design is the residual.

# 13498: 7-(29,14,60192)

• clan: 15-(32,16,6), 5 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 7-(28,13,19152) (# 13496) : der= 7-(28,13,19152) and res= 7-(28,14,41040) - the given design is the derived.

# 13499: 7-(30,14,86526)

• clan: 15-(32,16,6), 6 times reduced t, 2 times derived
• Tran van Trung construction (right) for 7-(29,13,26334) (# 13497) : der= 7-(29,13,26334) and res= 7-(29,14,60192) - the given design is the derived.
• Tran van Trung construction (left) for 7-(29,14,60192) (# 13498) : der= 7-(29,13,26334) and res= 7-(29,14,60192) - the given design is the residual.

created: Fri Oct 23 11:13:31 CEST 2009