t designs with small t, id ge 8100

# 8100: 5-(30,9,5300)

clan: 8-(31,10,106), 2 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(29,9,4452) (# 8099) : der= 5-(29,8,848) and res= 5-(29,9,4452) - the given design is the residual.

# 8101: 5-(28,9,3780)

clan: 8-(31,10,108), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
$Sp(6,2)$ (25 isom. types)
residual design of 6-(29,9,756) (# 12157)
derived from 6-(29,10,3780) (# 16003)
residual design of supplementary of 6-(29,9,1015) (# 16005)
derived from supplementary of 6-(29,10,5075) (# 16006)

# 8102: 5-(29,9,4536)

clan: 8-(31,10,108), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,3780) (# 8101) : der= 5-(28,8,756) and res= 5-(28,9,3780) - the given design is the residual.
design 6-(29,9,756) (# 12157) with respect to smaller t
derived from 6-(30,10,4536) (# 16002)
derived from supplementary of 6-(30,10,6090) (# 16004)
supplementary design of 6-(29,9,1015) (# 16005) with respect to smaller t

# 8103: 5-(28,9,3815)

clan: 8-(31,10,109), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
$Sp(6,2)$ (18 isom. types)
residual design of 6-(29,9,763) (# 16015)
derived from 6-(29,10,3815) (# 16016)
residual design of supplementary of 6-(29,9,1008) (# 16018)
derived from supplementary of 6-(29,10,5040) (# 16019)

# 8104: 5-(29,9,4578)

clan: 8-(31,10,109), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,3815) (# 8103) : der= 5-(28,8,763) and res= 5-(28,9,3815) - the given design is the residual.
derived from 6-(30,10,4578) (# 16014)
design 6-(29,9,763) (# 16015) with respect to smaller t
derived from supplementary of 6-(30,10,6048) (# 16017)
supplementary design of 6-(29,9,1008) (# 16018) with respect to smaller t

# 8105: 5-(28,9,3885)

clan: 8-(31,10,111), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8106: 5-(29,9,4662)

clan: 8-(31,10,111), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,3885) (# 8105) : der= 5-(28,8,777) and res= 5-(28,9,3885) - the given design is the residual.

# 8107: 5-(28,9,3920)

clan: 8-(31,10,112), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
$Sp(6,2)$ (28 isom. types)
residual design of 6-(29,9,784) (# 12161)
residual design of supplementary of 6-(29,9,987) (# 16054)

# 8108: 5-(29,9,4704)

clan: 8-(31,10,112), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,3920) (# 8107) : der= 5-(28,8,784) and res= 5-(28,9,3920) - the given design is the residual.
design 6-(29,9,784) (# 12161) with respect to smaller t
residual design of 6-(30,9,896) (# 12164)
derived from 6-(30,10,4704) (# 12246)
residual design of supplementary of 6-(30,9,1128) (# 16052)
supplementary design of 6-(29,9,987) (# 16054) with respect to smaller t

# 8109: 5-(30,9,5600)

clan: 8-(31,10,112), 2 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(29,9,4704) (# 8108) : der= 5-(29,8,896) and res= 5-(29,9,4704) - the given design is the residual.
design 6-(30,9,896) (# 12164) with respect to smaller t
derived from 6-(31,10,5600) (# 12251)
supplementary design of 6-(30,9,1128) (# 16052) with respect to smaller t

# 8110: 5-(28,9,3990)

clan: 8-(31,10,114), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
residual design of 6-(29,9,798) (# 12166)

# 8111: 5-(29,9,4788)

clan: 8-(31,10,114), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,3990) (# 8110) : der= 5-(28,8,798) and res= 5-(28,9,3990) - the given design is the residual.
design 6-(29,9,798) (# 12166) with respect to smaller t

# 8112: 5-(28,9,4025)

clan: 9-(31,10,10), 1 times reduced t, 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
Tran van Trung construction (right) for 5-(27,8,700) (# 11941) : der= 5-(27,8,700) and res= 5-(27,9,3325) - the given design is the derived.

# 8113: 5-(29,9,4830)

clan: 9-(31,10,10), 2 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,4025) (# 8112) : der= 5-(28,8,805) and res= 5-(28,9,4025) - the given design is the residual.

# 8114: 5-(28,9,4095)

clan: 8-(31,10,117), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
$Sp(6,2)$ (24 isom. types)
derived from 6-(29,10,4095) (# 11973)
residual design of 6-(29,9,819) (# 12169)
residual design of supplementary of 6-(29,9,952) (# 16031)
derived from supplementary of 6-(29,10,4760) (# 16032)

# 8115: 5-(29,9,4914)

clan: 8-(31,10,117), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,4095) (# 8114) : der= 5-(28,8,819) and res= 5-(28,9,4095) - the given design is the residual.
design 6-(29,9,819) (# 12169) with respect to smaller t
derived from 6-(30,10,4914) (# 12170)
derived from supplementary of 6-(30,10,5712) (# 16030)
supplementary design of 6-(29,9,952) (# 16031) with respect to smaller t

# 8116: 5-(28,9,4130)

clan: 8-(31,10,118), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
residual design of 6-(29,9,826) (# 12171)

# 8117: 5-(29,9,4956)

clan: 8-(31,10,118), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,4130) (# 8116) : der= 5-(28,8,826) and res= 5-(28,9,4130) - the given design is the residual.
design 6-(29,9,826) (# 12171) with respect to smaller t
derived from 6-(30,10,4956) (# 12254)

# 8118: 5-(28,9,420)

clan: 8-(31,10,12), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8119: 5-(29,9,504)

clan: 8-(31,10,12), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,420) (# 8118) : der= 5-(28,8,84) and res= 5-(28,9,420) - the given design is the residual.

# 8120: 5-(28,9,4200)

clan: 8-(31,10,120), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
residual design of 6-(29,9,840) (# 12174)

# 8121: 5-(29,9,5040)

clan: 8-(31,10,120), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,4200) (# 8120) : der= 5-(28,8,840) and res= 5-(28,9,4200) - the given design is the residual.
design 6-(29,9,840) (# 12174) with respect to smaller t
residual design of 6-(30,9,960) (# 12177)

# 8122: 5-(30,9,6000)

clan: 8-(31,10,120), 2 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(29,9,5040) (# 8121) : der= 5-(29,8,960) and res= 5-(29,9,5040) - the given design is the residual.
design 6-(30,9,960) (# 12177) with respect to smaller t

# 8123: 5-(28,9,4235)

clan: 21-(44,22,11), 13 times derived, 3 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
$Sp(6,2)$ (20 isom. types)
residual design of 6-(29,9,847) (# 16034)
derived from 6-(29,10,4235) (# 16035)
residual design of supplementary of 6-(29,9,924) (# 16037)
derived from supplementary of 6-(29,10,4620) (# 16038)

# 8124: 5-(29,9,5082)

clan: 21-(44,22,11), 1 times reduced t, 13 times derived, 2 times residual
Tran van Trung construction (left) for 5-(28,9,4235) (# 8123) : der= 5-(28,8,847) and res= 5-(28,9,4235) - the given design is the residual.
derived from 6-(30,10,5082) (# 12259)
design 6-(29,9,847) (# 16034) with respect to smaller t
derived from supplementary of 6-(30,10,5544) (# 16036)
supplementary design of 6-(29,9,924) (# 16037) with respect to smaller t

# 8125: 5-(28,9,4305)

clan: 8-(31,10,123), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
derived from 6-(29,10,4305) (# 11982)
residual design of 6-(29,9,861) (# 12179)
residual design of supplementary of 6-(29,9,910) (# 16044)
derived from supplementary of 6-(29,10,4550) (# 16045)

# 8126: 5-(29,9,5166)

clan: 8-(31,10,123), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,4305) (# 8125) : der= 5-(28,8,861) and res= 5-(28,9,4305) - the given design is the residual.
design 6-(29,9,861) (# 12179) with respect to smaller t
derived from 6-(30,10,5166) (# 12180)
derived from supplementary of 6-(30,10,5460) (# 16043)
supplementary design of 6-(29,9,910) (# 16044) with respect to smaller t

# 8127: 5-(30,9,6150)

clan: 8-(31,10,123), 2 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(29,9,5166) (# 8126) : der= 5-(29,8,984) and res= 5-(29,9,5166) - the given design is the residual.

# 8128: 5-(28,9,4340)

clan: 8-(31,10,124), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8129: 5-(29,9,5208)

clan: 8-(31,10,124), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,4340) (# 8128) : der= 5-(28,8,868) and res= 5-(28,9,4340) - the given design is the residual.

# 8130: 5-(28,9,455)

clan: 8-(31,10,13), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8131: 5-(29,9,546)

clan: 8-(31,10,13), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,455) (# 8130) : der= 5-(28,8,91) and res= 5-(28,9,455) - the given design is the residual.

# 8132: 5-(28,9,525)

clan: 8-(31,10,15), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
residual design of 6-(29,9,105) (# 12073)

# 8133: 5-(29,9,630)

clan: 8-(31,10,15), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,525) (# 8132) : der= 5-(28,8,105) and res= 5-(28,9,525) - the given design is the residual.
design 6-(29,9,105) (# 12073) with respect to smaller t

# 8134: 5-(30,9,750)

clan: 8-(31,10,15), 2 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(29,9,630) (# 8133) : der= 5-(29,8,120) and res= 5-(29,9,630) - the given design is the residual.

# 8135: 5-(28,9,560)

clan: 8-(31,10,16), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8136: 5-(29,9,672)

clan: 8-(31,10,16), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,560) (# 8135) : der= 5-(28,8,112) and res= 5-(28,9,560) - the given design is the residual.

# 8137: 5-(28,9,630)

clan: 8-(31,10,18), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
residual design of 6-(29,9,126) (# 12077)

# 8138: 5-(29,9,756)

clan: 8-(31,10,18), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,630) (# 8137) : der= 5-(28,8,126) and res= 5-(28,9,630) - the given design is the residual.
design 6-(29,9,126) (# 12077) with respect to smaller t

# 8139: 5-(28,9,665)

clan: 8-(31,10,19), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8140: 5-(29,9,798)

clan: 8-(31,10,19), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,665) (# 8139) : der= 5-(28,8,133) and res= 5-(28,9,665) - the given design is the residual.

# 8141: 5-(28,9,735)

clan: 8-(31,10,21), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8142: 5-(29,9,882)

clan: 8-(31,10,21), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,735) (# 8141) : der= 5-(28,8,147) and res= 5-(28,9,735) - the given design is the residual.

# 8143: 5-(30,9,1050)

clan: 8-(31,10,21), 2 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(29,9,882) (# 8142) : der= 5-(29,8,168) and res= 5-(29,9,882) - the given design is the residual.

# 8144: 5-(28,9,770)

clan: 21-(44,22,2), 13 times derived, 3 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
residual design of 6-(29,9,154) (# 12081)

# 8145: 5-(29,9,924)

clan: 21-(44,22,2), 1 times reduced t, 13 times derived, 2 times residual
Tran van Trung construction (left) for 5-(28,9,770) (# 8144) : der= 5-(28,8,154) and res= 5-(28,9,770) - the given design is the residual.
design 6-(29,9,154) (# 12081) with respect to smaller t

# 8146: 5-(30,9,1100)

clan: 21-(44,22,2), 2 times reduced t, 13 times derived, 1 times residual
Tran van Trung construction (left) for 5-(29,9,924) (# 8145) : der= 5-(29,8,176) and res= 5-(29,9,924) - the given design is the residual.
residual design of 6-(31,9,200) (# 12296)

# 8147: 5-(31,9,1300)

clan: 21-(44,22,2), 3 times reduced t, 13 times derived
Tran van Trung construction (left) for 5-(30,9,1100) (# 8146) : der= 5-(30,8,200) and res= 5-(30,9,1100) - the given design is the residual.
design 6-(31,9,200) (# 12296) with respect to smaller t

# 8148: 5-(28,9,840)

clan: 8-(31,10,24), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8149: 5-(29,9,1008)

clan: 8-(31,10,24), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,840) (# 8148) : der= 5-(28,8,168) and res= 5-(28,9,840) - the given design is the residual.

# 8150: 5-(28,9,875)

clan: 8-(31,10,25), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8151: 5-(29,9,1050)

clan: 8-(31,10,25), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,875) (# 8150) : der= 5-(28,8,175) and res= 5-(28,9,875) - the given design is the residual.

# 8152: 5-(28,9,945)

clan: 8-(31,10,27), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8153: 5-(29,9,1134)

clan: 8-(31,10,27), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,945) (# 8152) : der= 5-(28,8,189) and res= 5-(28,9,945) - the given design is the residual.

# 8154: 5-(28,9,980)

clan: 8-(31,10,28), 1 times derived, 2 times residual
$ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

# 8155: 5-(29,9,1176)

clan: 8-(31,10,28), 1 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction (left) for 5-(28,9,980) (# 8154) : der= 5-(28,8,196) and res= 5-(28,9,980) - the given design is the residual.

# 8156: 5-(30,9,1400)

clan: 8-(31,10,28), 2 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(29,9,1176) (# 8155) : der= 5-(29,8,224) and res= 5-(29,9,1176) - the given design is the residual.

# 8157: 5-(30,12,220)

clan: 11-(36,18,220), 6 times derived
\cite{MacWilliamsetal78}

# 8158: 5-(30,14,5390)

clan: 7-(32,16,5390), 2 times derived
\cite{MacWilliamsetal78}

# 8159: 5-(30,14,56375)

clan: 9-(32,16,6765), 2 times reduced t, 2 times derived
\cite{MacWilliamsetal78}

# 8160: 5-(30,6,5)

clan: 23-(48,24,5), 18 times derived
$\lambda=5$ $PSL(2,29)$ has 192 solutions (17 isom. types), $PGL(2,29)$ has 158 solutions (=158 isom. types)
\cite{Kreher95}

# 8161: 5-(30,7,150)

clan: 6-(30,7,12), 1 times reduced t
$PSL(2,29)$ many solutions, halving, Kreher 1995
design 6-(30,7,12) (# 12279) with respect to smaller t
supplementary design of 6-(30,7,12) (# 12279) with respect to smaller t
Tran van Trung construction (right) for 5-(29,6,12) (# 12280) : der= 5-(29,6,12) and res= 5-(29,7,138) - the given design is the derived.
Tran van Trung construction (left) for 5-(29,7,138) (# 12281) : der= 5-(29,6,12) and res= 5-(29,7,138) - the given design is the residual.

# 8162: 5-(30,7,90)

clan: 5-(30,7,90)
$PSL(2,29)$ $\ge 400000$ isomorphism types

# 8163: 5-(30,8,100)

clan: 21-(44,22,1), 2 times reduced t, 14 times derived
\cite{Kreher95}

# 8164: 5-(31,9,6370)

clan: 19-(44,22,980), 1 times reduced t, 13 times derived
$P\Gamma L(2,27) + C_3$

# 8165: 5-(32,6,3)

clan: 7-(34,8,3), 2 times derived
$S_4\times PSL(2,7)$ >= 10000 solutions

# 8166: 5-(32,6,6)

clan: 7-(34,8,6), 2 times derived
$PSL(2,31)$

# 8167: 5-(32,6,9)

clan: 25-(52,26,9), 20 times derived
$S_4\times PSL(2,7)$ >= 10000 solutions

# 8168: 5-(32,6,12)

clan: 7-(34,8,12), 2 times derived
$PSL(2,31)$

# 8169: 5-(32,7,15)

clan: 6-(33,8,15), 1 times derived
$PSL(2,31)$

# 8170: 5-(32,7,21)

clan: 6-(33,8,21), 1 times derived
$PSL(2,31)$

# 8171: 5-(32,7,30)

clan: 6-(33,8,30), 1 times derived
$PSL(2,31)$

# 8172: 5-(32,7,36)

# 8173: 5-(32,7,45)

clan: 10-(37,12,45), 5 times derived
$PSL(2,31)$

# 8174: 5-(32,7,51)

clan: 6-(33,8,51), 1 times derived
$PSL(2,31)$

# 8175: 5-(32,7,60)

clan: 6-(33,8,60), 1 times derived
$PSL(2,31)$

# 8176: 5-(32,7,63)

clan: 10-(37,12,63), 5 times derived
$S_4\times PSL(2,7)$

# 8177: 5-(32,7,66)

clan: 6-(33,8,66), 1 times derived
$PSL(2,31)$

# 8178: 5-(32,7,75)

clan: 6-(33,8,75), 1 times derived
$PSL(2,31)$

# 8179: 5-(32,7,78)

clan: 7-(34,8,6), 1 times derived, 1 times residual
$S_4\times PSL(2,7)$

# 8180: 5-(33,7,84)

clan: 7-(34,8,6), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(32,7,78) (# 8179) : der= 5-(32,6,6) and res= 5-(32,7,78) - the given design is the residual.

# 8181: 5-(32,7,81)

clan: 11-(37,12,6), 1 times reduced t, 5 times derived
$PSL(2,31)$
design 6-(32,7,6) (# 12353) with respect to smaller t
Tran van Trung construction (right) for 5-(31,6,6) (# 12354) : der= 5-(31,6,6) and res= 5-(31,7,75) - the given design is the derived.
Tran van Trung construction (left) for 5-(31,7,75) (# 12355) : der= 5-(31,6,6) and res= 5-(31,7,75) - the given design is the residual.

# 8182: 5-(32,7,84)

clan: 6-(33,8,84), 1 times derived
$S_4\times PSL(2,7)$

# 8183: 5-(32,7,90)

clan: 10-(37,12,90), 5 times derived
$PSL(2,31)$

# 8184: 5-(32,7,96)

clan: 6-(33,8,96), 1 times derived
$PSL(2,31)$

# 8185: 5-(32,7,99)

clan: 10-(37,12,99), 5 times derived
$S_4\times PSL(2,7)$

# 8186: 5-(32,7,105)

clan: 6-(33,8,105), 1 times derived
$PSL(2,31)$

# 8187: 5-(32,7,111)

clan: 6-(33,8,111), 1 times derived
$PSL(2,31)$

# 8188: 5-(32,7,120)

clan: 6-(33,8,120), 1 times derived
$PSL(2,31)$

# 8189: 5-(32,7,126)

clan: 10-(37,12,126), 5 times derived
$PSL(2,31)$

# 8190: 5-(32,7,135)

clan: 11-(37,12,10), 1 times reduced t, 5 times derived
$PSL(2,31)$
derived from 6-(33,8,135) (# 16191)
design 6-(32,7,10) (# 16192) with respect to smaller t
derived from supplementary of 6-(33,8,216) (# 16194)
supplementary design of 6-(32,7,16) (# 16195) with respect to smaller t
Tran van Trung construction (right) for 5-(31,6,10) (# 16200) : der= 5-(31,6,10) and res= 5-(31,7,125) - the given design is the derived.
Tran van Trung construction (left) for 5-(31,7,125) (# 16201) : der= 5-(31,6,10) and res= 5-(31,7,125) - the given design is the residual.

# 8191: 5-(32,7,141)

clan: 6-(33,8,141), 1 times derived
$PSL(2,31)$

# 8192: 5-(32,7,147)

clan: 6-(33,8,147), 1 times derived
$S_4\times PSL(2,7)$

# 8193: 5-(32,7,150)

clan: 6-(33,8,150), 1 times derived
$PSL(2,31)$

# 8194: 5-(32,7,156)

clan: 7-(34,8,12), 1 times derived, 1 times residual
$PSL(2,31)$

# 8195: 5-(33,7,168)

clan: 7-(34,8,12), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(32,7,156) (# 8194) : der= 5-(32,6,12) and res= 5-(32,7,156) - the given design is the residual.
\cite{Sebille98} $P\Gamma L(2,32)$

# 8196: 5-(32,7,162)

clan: 11-(37,12,12), 1 times reduced t, 5 times derived
$S_4\times PSL(2,7)$

# 8197: 5-(32,7,165)

clan: 6-(33,8,165), 1 times derived
$PSL(2,31)$

# 8198: 5-(32,7,168)

clan: 6-(33,8,168), 1 times derived
$S_4\times PSL(2,7)$

# 8199: 5-(32,7,171)

clan: 10-(37,12,171), 5 times derived
$PSL(2,31)$
derived from 6-(33,8,171) (# 16333)
derived from supplementary of 6-(33,8,180) (# 16335)

created: Fri Oct 23 11:11:37 CEST 2009