t designs with small t, id ge 18000

• clan: 8-(31,10,100)
• $PSL(3,5)$ (1658 isom. types) \cite{Bettenetal98}

# 18001: 7-(30,9,100)

• clan: 8-(31,10,100), 1 times derived
• derived from 8-(31,10,100) (# 18000)

# 18002: 7-(30,10,700)

• clan: 8-(31,10,100), 1 times residual
• residual design of 8-(31,10,100) (# 18000)

# 18003: 7-(31,10,1224)

• clan: 8-(31,10,153), 1 times reduced t
• supplementary design of 8-(31,10,100) (# 18000) with respect to smaller t
• Tran van Trung construction (right) for 7-(30,9,153) (# 18004) : der= 7-(30,9,153) and res= 7-(30,10,1071) - the given design is the derived.
• Tran van Trung construction (left) for 7-(30,10,1071) (# 18005) : der= 7-(30,9,153) and res= 7-(30,10,1071) - the given design is the residual.

# 18004: 7-(30,9,153)

• clan: 8-(31,10,153), 1 times derived
• derived from supplementary of 8-(31,10,100) (# 18000)

# 18005: 7-(30,10,1071)

• clan: 8-(31,10,153), 1 times residual
• residual design of supplementary of 8-(31,10,100) (# 18000)

# 18006: 6-(29,8,100)

• clan: 8-(31,10,100), 2 times derived
• derived from 7-(30,9,100) (# 18001)
• derived from supplementary of 7-(30,9,153) (# 18004)

# 18007: 6-(29,9,700)

• clan: 8-(31,10,100), 1 times derived, 1 times residual
• residual design of 7-(30,9,100) (# 18001)
• derived from 7-(30,10,700) (# 18002)
• residual design of supplementary of 7-(30,9,153) (# 18004)
• derived from supplementary of 7-(30,10,1071) (# 18005)

# 18008: 6-(29,8,153)

• clan: 8-(31,10,153), 2 times derived
• derived from supplementary of 7-(30,9,100) (# 18001)
• derived from 7-(30,9,153) (# 18004)

# 18009: 6-(29,9,1071)

• clan: 8-(31,10,153), 1 times derived, 1 times residual
• residual design of supplementary of 7-(30,9,100) (# 18001)
• derived from supplementary of 7-(30,10,700) (# 18002)
• residual design of 7-(30,9,153) (# 18004)
• derived from 7-(30,10,1071) (# 18005)

# 18010: 6-(29,10,3500)

• clan: 8-(31,10,100), 2 times residual
• residual design of 7-(30,10,700) (# 18002)
• residual design of supplementary of 7-(30,10,1071) (# 18005)

# 18011: 6-(29,10,5355)

• clan: 8-(31,10,153), 2 times residual
• residual design of supplementary of 7-(30,10,700) (# 18002)
• residual design of 7-(30,10,1071) (# 18005)

# 18012: 5-(28,7,153)

• clan: 8-(31,10,153), 3 times derived
• derived from supplementary of 6-(29,8,100) (# 18006)
• derived from 6-(29,8,153) (# 18008)

# 18013: 5-(28,8,1071)

• clan: 8-(31,10,153), 2 times derived, 1 times residual
• residual design of supplementary of 6-(29,8,100) (# 18006)
• derived from supplementary of 6-(29,9,700) (# 18007)
• residual design of 6-(29,8,153) (# 18008)
• derived from 6-(29,9,1071) (# 18009)

# 18014: 5-(28,9,5355)

• clan: 8-(31,10,153), 1 times derived, 2 times residual
• residual design of supplementary of 6-(29,9,700) (# 18007)
• residual design of 6-(29,9,1071) (# 18009)
• derived from supplementary of 6-(29,10,3500) (# 18010)
• derived from 6-(29,10,5355) (# 18011)

# 18015: 5-(28,10,13300)

• clan: 8-(31,10,100), 3 times residual
• residual design of 6-(29,10,3500) (# 18010)
• residual design of supplementary of 6-(29,10,5355) (# 18011)

# 18016: 5-(28,10,20349)

• clan: 8-(31,10,153), 3 times residual
• residual design of supplementary of 6-(29,10,3500) (# 18010)
• residual design of 6-(29,10,5355) (# 18011)

# 18017: 8-(31,10,93)

• clan: 8-(31,10,93)
• $PSL(3,5)$ (138 isom. types) \cite{Bettenetal98}

# 18018: 7-(30,9,93)

• clan: 8-(31,10,93), 1 times derived
• derived from 8-(31,10,93) (# 18017)

# 18019: 7-(30,10,651)

• clan: 8-(31,10,93), 1 times residual
• residual design of 8-(31,10,93) (# 18017)

# 18020: 7-(31,10,1280)

• clan: 8-(31,10,160), 1 times reduced t
• supplementary design of 8-(31,10,93) (# 18017) with respect to smaller t
• Tran van Trung construction (right) for 7-(30,9,160) (# 18021) : der= 7-(30,9,160) and res= 7-(30,10,1120) - the given design is the derived.
• Tran van Trung construction (left) for 7-(30,10,1120) (# 18022) : der= 7-(30,9,160) and res= 7-(30,10,1120) - the given design is the residual.

# 18021: 7-(30,9,160)

• clan: 8-(31,10,160), 1 times derived
• derived from supplementary of 8-(31,10,93) (# 18017)

# 18022: 7-(30,10,1120)

• clan: 8-(31,10,160), 1 times residual
• residual design of supplementary of 8-(31,10,93) (# 18017)

# 18023: 6-(29,8,93)

• clan: 8-(31,10,93), 2 times derived
• derived from 7-(30,9,93) (# 18018)
• derived from supplementary of 7-(30,9,160) (# 18021)

# 18024: 6-(29,9,651)

• clan: 8-(31,10,93), 1 times derived, 1 times residual
• residual design of 7-(30,9,93) (# 18018)
• derived from 7-(30,10,651) (# 18019)
• residual design of supplementary of 7-(30,9,160) (# 18021)
• derived from supplementary of 7-(30,10,1120) (# 18022)

# 18025: 6-(29,8,160)

• clan: 8-(31,10,160), 2 times derived
• derived from supplementary of 7-(30,9,93) (# 18018)
• derived from 7-(30,9,160) (# 18021)

# 18026: 6-(29,9,1120)

• clan: 8-(31,10,160), 1 times derived, 1 times residual
• residual design of supplementary of 7-(30,9,93) (# 18018)
• derived from supplementary of 7-(30,10,651) (# 18019)
• residual design of 7-(30,9,160) (# 18021)
• derived from 7-(30,10,1120) (# 18022)

# 18027: 6-(29,10,3255)

• clan: 8-(31,10,93), 2 times residual
• residual design of 7-(30,10,651) (# 18019)
• residual design of supplementary of 7-(30,10,1120) (# 18022)

# 18028: 6-(29,10,5600)

• clan: 8-(31,10,160), 2 times residual
• residual design of supplementary of 7-(30,10,651) (# 18019)
• residual design of 7-(30,10,1120) (# 18022)

# 18029: 5-(28,7,160)

• clan: 8-(31,10,160), 3 times derived
• derived from supplementary of 6-(29,8,93) (# 18023)
• derived from 6-(29,8,160) (# 18025)

# 18030: 5-(28,8,1120)

• clan: 8-(31,10,160), 2 times derived, 1 times residual
• residual design of supplementary of 6-(29,8,93) (# 18023)
• derived from supplementary of 6-(29,9,651) (# 18024)
• residual design of 6-(29,8,160) (# 18025)
• derived from 6-(29,9,1120) (# 18026)

# 18031: 5-(28,9,5600)

• clan: 8-(31,10,160), 1 times derived, 2 times residual
• residual design of supplementary of 6-(29,9,651) (# 18024)
• residual design of 6-(29,9,1120) (# 18026)
• derived from supplementary of 6-(29,10,3255) (# 18027)
• derived from 6-(29,10,5600) (# 18028)

# 18032: 5-(28,10,12369)

• clan: 8-(31,10,93), 3 times residual
• residual design of 6-(29,10,3255) (# 18027)
• residual design of supplementary of 6-(29,10,5600) (# 18028)

# 18033: 5-(28,10,21280)

• clan: 8-(31,10,160), 3 times residual
• residual design of supplementary of 6-(29,10,3255) (# 18027)
• residual design of 6-(29,10,5600) (# 18028)

# 18034: 8-(31,12,3080)

• clan: 21-(44,22,8), 10 times derived, 3 times residual
• $PSL(3,5)$ ($\ge 107$ isom. types)

# 18035: 7-(31,12,14784)

• clan: 21-(44,22,8), 1 times reduced t, 10 times derived, 3 times residual
• design 8-(31,12,3080) (# 18034) with respect to smaller t
• Tran van Trung construction (right) for 7-(30,11,3080) (# 18036) : der= 7-(30,11,3080) and res= 7-(30,12,11704) - the given design is the derived.
• Tran van Trung construction (left) for 7-(30,12,11704) (# 18037) : der= 7-(30,11,3080) and res= 7-(30,12,11704) - the given design is the residual.

# 18036: 7-(30,11,3080)

• clan: 21-(44,22,8), 11 times derived, 3 times residual
• derived from 8-(31,12,3080) (# 18034)

# 18037: 7-(30,12,11704)

• clan: 21-(44,22,8), 10 times derived, 4 times residual
• residual design of 8-(31,12,3080) (# 18034)

# 18038: 7-(31,12,27720)

• clan: 21-(44,22,15), 1 times reduced t, 10 times derived, 3 times residual
• supplementary design of 8-(31,12,3080) (# 18034) with respect to smaller t
• Tran van Trung construction (right) for 7-(30,11,5775) (# 18039) : der= 7-(30,11,5775) and res= 7-(30,12,21945) - the given design is the derived.
• Tran van Trung construction (left) for 7-(30,12,21945) (# 18040) : der= 7-(30,11,5775) and res= 7-(30,12,21945) - the given design is the residual.

# 18039: 7-(30,11,5775)

• clan: 21-(44,22,15), 11 times derived, 3 times residual
• derived from supplementary of 8-(31,12,3080) (# 18034)

# 18040: 7-(30,12,21945)

• clan: 21-(44,22,15), 10 times derived, 4 times residual
• residual design of supplementary of 8-(31,12,3080) (# 18034)

# 18041: 6-(31,12,61600)

• clan: 21-(44,22,8), 2 times reduced t, 10 times derived, 3 times residual
• design 7-(31,12,14784) (# 18035) with respect to smaller t
• supplementary design of 7-(31,12,27720) (# 18038) with respect to smaller t
• Tran van Trung construction (right) for 6-(30,11,14784) (# 18042) : der= 6-(30,11,14784) and res= 6-(30,12,46816) - the given design is the derived.
• Tran van Trung construction (left) for 6-(30,12,46816) (# 18043) : der= 6-(30,11,14784) and res= 6-(30,12,46816) - the given design is the residual.

# 18042: 6-(30,11,14784)

• clan: 21-(44,22,8), 1 times reduced t, 11 times derived, 3 times residual
• derived from 7-(31,12,14784) (# 18035)
• design 7-(30,11,3080) (# 18036) with respect to smaller t
• derived from supplementary of 7-(31,12,27720) (# 18038)
• supplementary design of 7-(30,11,5775) (# 18039) with respect to smaller t
• Tran van Trung construction (right) for 6-(29,10,3080) (# 18047) : der= 6-(29,10,3080) and res= 6-(29,11,11704) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,11,11704) (# 18048) : der= 6-(29,10,3080) and res= 6-(29,11,11704) - the given design is the residual.

# 18043: 6-(30,12,46816)

• clan: 21-(44,22,8), 1 times reduced t, 10 times derived, 4 times residual
• residual design of 7-(31,12,14784) (# 18035)
• design 7-(30,12,11704) (# 18037) with respect to smaller t
• residual design of supplementary of 7-(31,12,27720) (# 18038)
• supplementary design of 7-(30,12,21945) (# 18040) with respect to smaller t
• Tran van Trung construction (right) for 6-(29,11,11704) (# 18048) : der= 6-(29,11,11704) and res= 6-(29,12,35112) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,12,35112) (# 18051) : der= 6-(29,11,11704) and res= 6-(29,12,35112) - the given design is the residual.

# 18044: 6-(31,12,115500)

• clan: 21-(44,22,15), 2 times reduced t, 10 times derived, 3 times residual
• supplementary design of 7-(31,12,14784) (# 18035) with respect to smaller t
• design 7-(31,12,27720) (# 18038) with respect to smaller t
• Tran van Trung construction (right) for 6-(30,11,27720) (# 18045) : der= 6-(30,11,27720) and res= 6-(30,12,87780) - the given design is the derived.
• Tran van Trung construction (left) for 6-(30,12,87780) (# 18046) : der= 6-(30,11,27720) and res= 6-(30,12,87780) - the given design is the residual.

# 18045: 6-(30,11,27720)

• clan: 21-(44,22,15), 1 times reduced t, 11 times derived, 3 times residual
• derived from supplementary of 7-(31,12,14784) (# 18035)
• supplementary design of 7-(30,11,3080) (# 18036) with respect to smaller t
• derived from 7-(31,12,27720) (# 18038)
• design 7-(30,11,5775) (# 18039) with respect to smaller t
• Tran van Trung construction (right) for 6-(29,10,5775) (# 18049) : der= 6-(29,10,5775) and res= 6-(29,11,21945) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,11,21945) (# 18050) : der= 6-(29,10,5775) and res= 6-(29,11,21945) - the given design is the residual.

# 18046: 6-(30,12,87780)

• clan: 21-(44,22,15), 1 times reduced t, 10 times derived, 4 times residual
• residual design of supplementary of 7-(31,12,14784) (# 18035)
• supplementary design of 7-(30,12,11704) (# 18037) with respect to smaller t
• residual design of 7-(31,12,27720) (# 18038)
• design 7-(30,12,21945) (# 18040) with respect to smaller t
• Tran van Trung construction (right) for 6-(29,11,21945) (# 18050) : der= 6-(29,11,21945) and res= 6-(29,12,65835) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,12,65835) (# 18052) : der= 6-(29,11,21945) and res= 6-(29,12,65835) - the given design is the residual.

# 18047: 6-(29,10,3080)

• clan: 21-(44,22,8), 12 times derived, 3 times residual
• derived from 7-(30,11,3080) (# 18036)
• derived from supplementary of 7-(30,11,5775) (# 18039)

# 18048: 6-(29,11,11704)

• clan: 21-(44,22,8), 11 times derived, 4 times residual
• residual design of 7-(30,11,3080) (# 18036)
• derived from 7-(30,12,11704) (# 18037)
• residual design of supplementary of 7-(30,11,5775) (# 18039)
• derived from supplementary of 7-(30,12,21945) (# 18040)

# 18049: 6-(29,10,5775)

• clan: 21-(44,22,15), 12 times derived, 3 times residual
• derived from supplementary of 7-(30,11,3080) (# 18036)
• derived from 7-(30,11,5775) (# 18039)

# 18050: 6-(29,11,21945)

• clan: 21-(44,22,15), 11 times derived, 4 times residual
• residual design of supplementary of 7-(30,11,3080) (# 18036)
• derived from supplementary of 7-(30,12,11704) (# 18037)
• residual design of 7-(30,11,5775) (# 18039)
• derived from 7-(30,12,21945) (# 18040)

# 18051: 6-(29,12,35112)

• clan: 21-(44,22,8), 10 times derived, 5 times residual
• residual design of 7-(30,12,11704) (# 18037)
• residual design of supplementary of 7-(30,12,21945) (# 18040)

# 18052: 6-(29,12,65835)

• clan: 21-(44,22,15), 10 times derived, 5 times residual
• residual design of supplementary of 7-(30,12,11704) (# 18037)
• residual design of 7-(30,12,21945) (# 18040)

# 18053: 5-(31,12,228800)

• clan: 21-(44,22,8), 3 times reduced t, 10 times derived, 3 times residual
• design 6-(31,12,61600) (# 18041) with respect to smaller t
• supplementary design of 6-(31,12,115500) (# 18044) with respect to smaller t
• Tran van Trung construction (right) for 5-(30,11,61600) (# 18054) : der= 5-(30,11,61600) and res= 5-(30,12,167200) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,12,167200) (# 18055) : der= 5-(30,11,61600) and res= 5-(30,12,167200) - the given design is the residual.

# 18054: 5-(30,11,61600)

• clan: 21-(44,22,8), 2 times reduced t, 11 times derived, 3 times residual
• derived from 6-(31,12,61600) (# 18041)
• design 6-(30,11,14784) (# 18042) with respect to smaller t
• derived from supplementary of 6-(31,12,115500) (# 18044)
• supplementary design of 6-(30,11,27720) (# 18045) with respect to smaller t
• Tran van Trung construction (right) for 5-(29,10,14784) (# 18059) : der= 5-(29,10,14784) and res= 5-(29,11,46816) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,11,46816) (# 18060) : der= 5-(29,10,14784) and res= 5-(29,11,46816) - the given design is the residual.

# 18055: 5-(30,12,167200)

• clan: 21-(44,22,8), 2 times reduced t, 10 times derived, 4 times residual
• residual design of 6-(31,12,61600) (# 18041)
• design 6-(30,12,46816) (# 18043) with respect to smaller t
• residual design of supplementary of 6-(31,12,115500) (# 18044)
• supplementary design of 6-(30,12,87780) (# 18046) with respect to smaller t
• Tran van Trung construction (right) for 5-(29,11,46816) (# 18060) : der= 5-(29,11,46816) and res= 5-(29,12,120384) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,12,120384) (# 18063) : der= 5-(29,11,46816) and res= 5-(29,12,120384) - the given design is the residual.

# 18056: 5-(31,12,429000)

• clan: 21-(44,22,15), 3 times reduced t, 10 times derived, 3 times residual
• supplementary design of 6-(31,12,61600) (# 18041) with respect to smaller t
• design 6-(31,12,115500) (# 18044) with respect to smaller t
• Tran van Trung construction (right) for 5-(30,11,115500) (# 18057) : der= 5-(30,11,115500) and res= 5-(30,12,313500) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,12,313500) (# 18058) : der= 5-(30,11,115500) and res= 5-(30,12,313500) - the given design is the residual.

# 18057: 5-(30,11,115500)

• clan: 21-(44,22,15), 2 times reduced t, 11 times derived, 3 times residual
• derived from supplementary of 6-(31,12,61600) (# 18041)
• supplementary design of 6-(30,11,14784) (# 18042) with respect to smaller t
• derived from 6-(31,12,115500) (# 18044)
• design 6-(30,11,27720) (# 18045) with respect to smaller t
• Tran van Trung construction (right) for 5-(29,10,27720) (# 18061) : der= 5-(29,10,27720) and res= 5-(29,11,87780) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,11,87780) (# 18062) : der= 5-(29,10,27720) and res= 5-(29,11,87780) - the given design is the residual.

# 18058: 5-(30,12,313500)

• clan: 21-(44,22,15), 2 times reduced t, 10 times derived, 4 times residual
• residual design of supplementary of 6-(31,12,61600) (# 18041)
• supplementary design of 6-(30,12,46816) (# 18043) with respect to smaller t
• residual design of 6-(31,12,115500) (# 18044)
• design 6-(30,12,87780) (# 18046) with respect to smaller t
• Tran van Trung construction (right) for 5-(29,11,87780) (# 18062) : der= 5-(29,11,87780) and res= 5-(29,12,225720) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,12,225720) (# 18064) : der= 5-(29,11,87780) and res= 5-(29,12,225720) - the given design is the residual.

# 18059: 5-(29,10,14784)

• clan: 21-(44,22,8), 1 times reduced t, 12 times derived, 3 times residual
• derived from 6-(30,11,14784) (# 18042)
• derived from supplementary of 6-(30,11,27720) (# 18045)
• design 6-(29,10,3080) (# 18047) with respect to smaller t
• supplementary design of 6-(29,10,5775) (# 18049) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,11704) (# 18065) : der= 5-(28,9,3080) and res= 5-(28,10,11704) - the given design is the residual.

# 18060: 5-(29,11,46816)

• clan: 21-(44,22,8), 1 times reduced t, 11 times derived, 4 times residual
• residual design of 6-(30,11,14784) (# 18042)
• derived from 6-(30,12,46816) (# 18043)
• residual design of supplementary of 6-(30,11,27720) (# 18045)
• derived from supplementary of 6-(30,12,87780) (# 18046)
• design 6-(29,11,11704) (# 18048) with respect to smaller t
• supplementary design of 6-(29,11,21945) (# 18050) with respect to smaller t
• Tran van Trung construction (right) for 5-(28,10,11704) (# 18065) : der= 5-(28,10,11704) and res= 5-(28,11,35112) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,11,35112) (# 18068) : der= 5-(28,10,11704) and res= 5-(28,11,35112) - the given design is the residual.

# 18061: 5-(29,10,27720)

• clan: 21-(44,22,15), 1 times reduced t, 12 times derived, 3 times residual
• derived from supplementary of 6-(30,11,14784) (# 18042)
• derived from 6-(30,11,27720) (# 18045)
• supplementary design of 6-(29,10,3080) (# 18047) with respect to smaller t
• design 6-(29,10,5775) (# 18049) with respect to smaller t
• Tran van Trung construction (right) for 5-(28,9,5775) (# 18066) : der= 5-(28,9,5775) and res= 5-(28,10,21945) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,10,21945) (# 18067) : der= 5-(28,9,5775) and res= 5-(28,10,21945) - the given design is the residual.

# 18062: 5-(29,11,87780)

• clan: 21-(44,22,15), 1 times reduced t, 11 times derived, 4 times residual
• residual design of supplementary of 6-(30,11,14784) (# 18042)
• derived from supplementary of 6-(30,12,46816) (# 18043)
• residual design of 6-(30,11,27720) (# 18045)
• derived from 6-(30,12,87780) (# 18046)
• supplementary design of 6-(29,11,11704) (# 18048) with respect to smaller t
• design 6-(29,11,21945) (# 18050) with respect to smaller t
• Tran van Trung construction (right) for 5-(28,10,21945) (# 18067) : der= 5-(28,10,21945) and res= 5-(28,11,65835) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,11,65835) (# 18069) : der= 5-(28,10,21945) and res= 5-(28,11,65835) - the given design is the residual.

# 18063: 5-(29,12,120384)

• clan: 21-(44,22,8), 1 times reduced t, 10 times derived, 5 times residual
• residual design of 6-(30,12,46816) (# 18043)
• residual design of supplementary of 6-(30,12,87780) (# 18046)
• design 6-(29,12,35112) (# 18051) with respect to smaller t
• supplementary design of 6-(29,12,65835) (# 18052) with respect to smaller t
• Tran van Trung construction (right) for 5-(28,11,35112) (# 18068) : der= 5-(28,11,35112) and res= 5-(28,12,85272) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,12,85272) (# 18070) : der= 5-(28,11,35112) and res= 5-(28,12,85272) - the given design is the residual.

# 18064: 5-(29,12,225720)

• clan: 21-(44,22,15), 1 times reduced t, 10 times derived, 5 times residual
• residual design of supplementary of 6-(30,12,46816) (# 18043)
• residual design of 6-(30,12,87780) (# 18046)
• supplementary design of 6-(29,12,35112) (# 18051) with respect to smaller t
• design 6-(29,12,65835) (# 18052) with respect to smaller t
• Tran van Trung construction (right) for 5-(28,11,65835) (# 18069) : der= 5-(28,11,65835) and res= 5-(28,12,159885) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,12,159885) (# 18071) : der= 5-(28,11,65835) and res= 5-(28,12,159885) - the given design is the residual.

# 18065: 5-(28,10,11704)

• clan: 21-(44,22,8), 12 times derived, 4 times residual
• residual design of 6-(29,10,3080) (# 18047)
• derived from 6-(29,11,11704) (# 18048)
• residual design of supplementary of 6-(29,10,5775) (# 18049)
• derived from supplementary of 6-(29,11,21945) (# 18050)

# 18066: 5-(28,9,5775)

• clan: 21-(44,22,15), 13 times derived, 3 times residual
• derived from supplementary of 6-(29,10,3080) (# 18047)
• derived from 6-(29,10,5775) (# 18049)

# 18067: 5-(28,10,21945)

• clan: 21-(44,22,15), 12 times derived, 4 times residual
• residual design of supplementary of 6-(29,10,3080) (# 18047)
• derived from supplementary of 6-(29,11,11704) (# 18048)
• residual design of 6-(29,10,5775) (# 18049)
• derived from 6-(29,11,21945) (# 18050)

# 18068: 5-(28,11,35112)

• clan: 21-(44,22,8), 11 times derived, 5 times residual
• residual design of 6-(29,11,11704) (# 18048)
• residual design of supplementary of 6-(29,11,21945) (# 18050)
• derived from 6-(29,12,35112) (# 18051)
• derived from supplementary of 6-(29,12,65835) (# 18052)

# 18069: 5-(28,11,65835)

• clan: 21-(44,22,15), 11 times derived, 5 times residual
• residual design of supplementary of 6-(29,11,11704) (# 18048)
• residual design of 6-(29,11,21945) (# 18050)
• derived from supplementary of 6-(29,12,35112) (# 18051)
• derived from 6-(29,12,65835) (# 18052)

# 18070: 5-(28,12,85272)

• clan: 21-(44,22,8), 10 times derived, 6 times residual
• residual design of 6-(29,12,35112) (# 18051)
• residual design of supplementary of 6-(29,12,65835) (# 18052)

# 18071: 5-(28,12,159885)

• clan: 21-(44,22,15), 10 times derived, 6 times residual
• residual design of supplementary of 6-(29,12,35112) (# 18051)
• residual design of 6-(29,12,65835) (# 18052)

# 18072: 5-(30,10,18480)

• clan: 21-(44,22,8), 2 times reduced t, 12 times derived, 2 times residual
• Tran van Trung construction (left) for 5-(29,10,14784) (# 18059) : der= 5-(29,9,3696) and res= 5-(29,10,14784) - the given design is the residual.

# 18073: 5-(31,10,22880)

• clan: 21-(44,22,8), 3 times reduced t, 12 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(30,10,18480) (# 18072) : der= 5-(30,9,4400) and res= 5-(30,10,18480) - the given design is the residual.

# 18074: 5-(31,11,80080)

• clan: 21-(44,22,8), 3 times reduced t, 11 times derived, 2 times residual
• Tran van Trung construction (right) for 5-(30,10,18480) (# 18072) : der= 5-(30,10,18480) and res= 5-(30,11,61600) - the given design is the derived.

# 18075: 5-(32,10,28080)

• clan: 21-(44,22,8), 4 times reduced t, 12 times derived
• Tran van Trung construction (left) for 5-(31,10,22880) (# 18073) : der= 5-(31,9,5200) and res= 5-(31,10,22880) - the given design is the residual.

# 18076: 5-(32,11,102960)

• clan: 21-(44,22,8), 4 times reduced t, 11 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(31,10,22880) (# 18073) : der= 5-(31,10,22880) and res= 5-(31,11,80080) - the given design is the derived.
• Tran van Trung construction (left) for 5-(31,11,80080) (# 18074) : der= 5-(31,10,22880) and res= 5-(31,11,80080) - the given design is the residual.

# 18077: 5-(32,12,308880)

• clan: 21-(44,22,8), 4 times reduced t, 10 times derived, 2 times residual
• Tran van Trung construction (right) for 5-(31,11,80080) (# 18074) : der= 5-(31,11,80080) and res= 5-(31,12,228800) - the given design is the derived.

# 18078: 5-(33,11,131040)

• clan: 21-(44,22,8), 5 times reduced t, 11 times derived
• Tran van Trung construction (right) for 5-(32,10,28080) (# 18075) : der= 5-(32,10,28080) and res= 5-(32,11,102960) - the given design is the derived.
• Tran van Trung construction (left) for 5-(32,11,102960) (# 18076) : der= 5-(32,10,28080) and res= 5-(32,11,102960) - the given design is the residual.

# 18079: 5-(33,12,411840)

• clan: 21-(44,22,8), 5 times reduced t, 10 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(32,11,102960) (# 18076) : der= 5-(32,11,102960) and res= 5-(32,12,308880) - the given design is the derived.
• Tran van Trung construction (left) for 5-(32,12,308880) (# 18077) : der= 5-(32,11,102960) and res= 5-(32,12,308880) - the given design is the residual.

# 18080: 5-(34,12,542880)

• clan: 21-(44,22,8), 6 times reduced t, 10 times derived
• Tran van Trung construction (right) for 5-(33,11,131040) (# 18078) : der= 5-(33,11,131040) and res= 5-(33,12,411840) - the given design is the derived.
• Tran van Trung construction (left) for 5-(33,12,411840) (# 18079) : der= 5-(33,11,131040) and res= 5-(33,12,411840) - the given design is the residual.

# 18081: 8-(36,11,1260)

• clan: 11-(37,12,10), 2 times reduced t, 1 times derived
• $Sp(6,2)_36$ (many isomorphism types) Betten, Laue, Suleiman, Wassermann 1997

# 18082: 7-(35,11,7875)

• clan: 11-(37,12,10), 2 times reduced t, 1 times derived, 1 times residual
• residual design of 8-(36,11,1260) (# 18081)

# 18083: 7-(36,11,14616)

• clan: 11-(37,12,16), 3 times reduced t, 1 times derived
• supplementary design of 8-(36,11,1260) (# 18081) with respect to smaller t
• Tran van Trung construction (right) for 7-(35,10,2016) (# 18084) : der= 7-(35,10,2016) and res= 7-(35,11,12600) - the given design is the derived.
• Tran van Trung construction (left) for 7-(35,11,12600) (# 18085) : der= 7-(35,10,2016) and res= 7-(35,11,12600) - the given design is the residual.

# 18084: 7-(35,10,2016)

• clan: 11-(37,12,16), 2 times reduced t, 2 times derived
• derived from supplementary of 8-(36,11,1260) (# 18081)

# 18085: 7-(35,11,12600)

• clan: 11-(37,12,16), 2 times reduced t, 1 times derived, 1 times residual
• residual design of supplementary of 8-(36,11,1260) (# 18081)

# 18086: 6-(34,11,37800)

• clan: 11-(37,12,10), 2 times reduced t, 1 times derived, 2 times residual
• residual design of 7-(35,11,7875) (# 18082)
• residual design of supplementary of 7-(35,11,12600) (# 18085)

# 18087: 6-(34,11,60480)

• clan: 11-(37,12,16), 2 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 7-(35,11,7875) (# 18082)
• residual design of 7-(35,11,12600) (# 18085)

# 18088: 5-(33,11,144900)

• clan: 11-(37,12,10), 2 times reduced t, 1 times derived, 3 times residual
• residual design of 6-(34,11,37800) (# 18086)
• residual design of supplementary of 6-(34,11,60480) (# 18087)

# 18089: 5-(33,11,231840)

• clan: 11-(37,12,16), 2 times reduced t, 1 times derived, 3 times residual
• residual design of supplementary of 6-(34,11,37800) (# 18086)
• residual design of 6-(34,11,60480) (# 18087)

# 18090: 8-(40,11,1440)

• clan: 29-(60,30,9), 1 times reduced t, 19 times derived, 1 times residual
• $PSL(4,3)$ (>= $2^{31}$ isomorphism types) Betten, Laue, Wassermann 1997

# 18091: 7-(40,11,11880)

• clan: 29-(60,30,9), 2 times reduced t, 19 times derived, 1 times residual
• design 8-(40,11,1440) (# 18090) with respect to smaller t
• Tran van Trung construction (right) for 7-(39,10,1440) (# 18092) : der= 7-(39,10,1440) and res= 7-(39,11,10440) - the given design is the derived.
• Tran van Trung construction (left) for 7-(39,11,10440) (# 18093) : der= 7-(39,10,1440) and res= 7-(39,11,10440) - the given design is the residual.

# 18092: 7-(39,10,1440)

• clan: 29-(60,30,9), 1 times reduced t, 20 times derived, 1 times residual
• derived from 8-(40,11,1440) (# 18090)

# 18093: 7-(39,11,10440)

• clan: 29-(60,30,9), 1 times reduced t, 19 times derived, 2 times residual
• residual design of 8-(40,11,1440) (# 18090)

# 18094: 7-(40,11,29040)

• clan: 29-(60,30,22), 2 times reduced t, 19 times derived, 1 times residual
• supplementary design of 8-(40,11,1440) (# 18090) with respect to smaller t
• Tran van Trung construction (right) for 7-(39,10,3520) (# 18095) : der= 7-(39,10,3520) and res= 7-(39,11,25520) - the given design is the derived.
• Tran van Trung construction (left) for 7-(39,11,25520) (# 18096) : der= 7-(39,10,3520) and res= 7-(39,11,25520) - the given design is the residual.

# 18095: 7-(39,10,3520)

• clan: 29-(60,30,22), 1 times reduced t, 20 times derived, 1 times residual
• derived from supplementary of 8-(40,11,1440) (# 18090)

# 18096: 7-(39,11,25520)

• clan: 29-(60,30,22), 1 times reduced t, 19 times derived, 2 times residual
• residual design of supplementary of 8-(40,11,1440) (# 18090)

# 18097: 6-(40,11,80784)

• clan: 29-(60,30,9), 3 times reduced t, 19 times derived, 1 times residual
• design 7-(40,11,11880) (# 18091) with respect to smaller t
• supplementary design of 7-(40,11,29040) (# 18094) with respect to smaller t
• Tran van Trung construction (right) for 6-(39,10,11880) (# 18098) : der= 6-(39,10,11880) and res= 6-(39,11,68904) - the given design is the derived.
• Tran van Trung construction (left) for 6-(39,11,68904) (# 18099) : der= 6-(39,10,11880) and res= 6-(39,11,68904) - the given design is the residual.

# 18098: 6-(39,10,11880)

• clan: 29-(60,30,9), 2 times reduced t, 20 times derived, 1 times residual
• derived from 7-(40,11,11880) (# 18091)
• design 7-(39,10,1440) (# 18092) with respect to smaller t
• derived from supplementary of 7-(40,11,29040) (# 18094)
• supplementary design of 7-(39,10,3520) (# 18095) with respect to smaller t
• Tran van Trung construction (right) for 6-(38,9,1440) (# 18103) : der= 6-(38,9,1440) and res= 6-(38,10,10440) - the given design is the derived.
• Tran van Trung construction (left) for 6-(38,10,10440) (# 18104) : der= 6-(38,9,1440) and res= 6-(38,10,10440) - the given design is the residual.

# 18099: 6-(39,11,68904)

• clan: 29-(60,30,9), 2 times reduced t, 19 times derived, 2 times residual
• residual design of 7-(40,11,11880) (# 18091)
• design 7-(39,11,10440) (# 18093) with respect to smaller t
• residual design of supplementary of 7-(40,11,29040) (# 18094)
• supplementary design of 7-(39,11,25520) (# 18096) with respect to smaller t
• Tran van Trung construction (right) for 6-(38,10,10440) (# 18104) : der= 6-(38,10,10440) and res= 6-(38,11,58464) - the given design is the derived.
• Tran van Trung construction (left) for 6-(38,11,58464) (# 18107) : der= 6-(38,10,10440) and res= 6-(38,11,58464) - the given design is the residual.

created: Fri Oct 23 11:14:51 CEST 2009