clan: 6-(25,8,15), 1 times reduced t
Tran van Trung construction (left) for 5-(24,8,85) (# 6137) : der= 5-(24,7,15) and res= 5-(24,8,85) - the given design is the residual.

# 6139: 5-(24,8,850)

clan: 6-(25,8,150), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6140: 5-(24,8,851)

clan: 5-(24,8,851)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6141: 5-(24,8,852)

clan: 13-(32,16,852), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6142: 5-(24,8,853)

clan: 5-(24,8,853)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6143: 5-(24,8,854)

clan: 5-(24,8,854)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6144: 5-(24,8,855)

clan: 15-(32,16,15), 2 times reduced t, 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6145: 5-(24,8,856)

clan: 5-(24,8,856)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6146: 5-(24,8,857)

clan: 5-(24,8,857)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6147: 5-(24,8,858)

clan: 13-(32,16,858), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6148: 5-(24,8,859)

clan: 5-(24,8,859)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6149: 5-(24,8,86)

clan: 5-(24,8,86)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6150: 5-(24,8,860)

clan: 5-(24,8,860)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6151: 5-(24,8,861)

clan: 13-(32,16,861), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6152: 5-(24,8,862)

clan: 5-(24,8,862)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6153: 5-(24,8,863)

clan: 5-(24,8,863)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6154: 5-(24,8,864)

clan: 13-(32,16,864), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,105) (# 10414)

# 6155: 5-(24,8,865)

clan: 5-(24,8,865)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6156: 5-(24,8,866)

clan: 5-(24,8,866)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6157: 5-(24,8,867)

clan: 17-(36,18,17), 10 times derived, 2 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6158: 5-(24,8,868)

clan: 5-(24,8,868)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6159: 5-(24,8,869)

clan: 5-(24,8,869)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6160: 5-(24,8,87)

clan: 13-(32,16,87), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6161: 5-(24,8,870)

clan: 13-(32,16,870), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6162: 5-(24,8,871)

clan: 5-(24,8,871)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6163: 5-(24,8,872)

clan: 5-(24,8,872)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6164: 5-(24,8,873)

clan: 13-(32,16,873), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6165: 5-(24,8,874)

clan: 6-(24,8,138), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6166: 5-(24,8,875)

clan: 5-(24,8,875)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6167: 5-(24,8,876)

clan: 13-(32,16,876), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6168: 5-(24,8,877)

clan: 5-(24,8,877)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6169: 5-(24,8,878)

clan: 5-(24,8,878)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6170: 5-(24,8,879)

clan: 13-(32,16,879), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6171: 5-(24,8,88)

clan: 5-(24,8,88)
$PGL(2,23)$

# 6172: 5-(24,8,880)

clan: 5-(24,8,880)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6173: 5-(24,8,881)

clan: 5-(24,8,881)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6174: 5-(24,8,882)

clan: 13-(32,16,882), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6175: 5-(24,8,883)

clan: 5-(24,8,883)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6176: 5-(24,8,884)

clan: 6-(25,8,156), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6177: 5-(24,8,885)

clan: 13-(32,16,885), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6178: 5-(24,8,89)

clan: 5-(24,8,89)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6179: 5-(24,8,9)

clan: 13-(32,16,9), 8 times derived
\cite{KramerMagliveras74}

# 6180: 5-(24,8,90)

clan: 13-(32,16,90), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6181: 5-(24,8,91)

clan: 5-(24,8,91)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6182: 5-(24,8,92)

clan: 5-(24,8,92)
$PGL(2,23)$

# 6183: 5-(24,8,93)

clan: 13-(32,16,93), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6184: 5-(24,8,94)

clan: 5-(24,8,94)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6185: 5-(24,8,95)

clan: 6-(24,8,15), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6186: 5-(24,8,96)

clan: 13-(32,16,96), 8 times derived
$PGL(2,23)$

# 6187: 5-(24,8,97)

clan: 5-(24,8,97)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6188: 5-(24,8,98)

clan: 5-(24,8,98)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6189: 5-(24,8,99)

clan: 13-(32,16,99), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6190: 5-(24,9,1002)

clan: 11-(30,15,1002), 6 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6191: 5-(25,10,4008)

clan: 11-(30,15,1002), 1 times reduced t, 5 times derived
Tran van Trung construction (right) for 5-(24,9,1002) (# 6190) : der= 5-(24,9,1002) and res= 5-(24,10,3006) - the given design is the derived.

# 6192: 5-(24,9,1008)

clan: 13-(32,16,252), 7 times derived, 1 times residual
$PGL(2,23)$ (>1 isomorphism types)

# 6193: 5-(25,9,1260)

clan: 13-(32,16,252), 1 times reduced t, 7 times derived
Tran van Trung construction (left) for 5-(24,9,1008) (# 6192) : der= 5-(24,8,252) and res= 5-(24,9,1008) - the given design is the residual.

# 6194: 5-(25,10,4032)

clan: 13-(32,16,252), 1 times reduced t, 6 times derived, 1 times residual
Tran van Trung construction (right) for 5-(24,9,1008) (# 6192) : der= 5-(24,9,1008) and res= 5-(24,10,3024) - the given design is the derived.

# 6195: 5-(26,10,5292)

clan: 13-(32,16,252), 2 times reduced t, 6 times derived
Tran van Trung construction (right) for 5-(25,9,1260) (# 6193) : der= 5-(25,9,1260) and res= 5-(25,10,4032) - the given design is the derived.
Tran van Trung construction (left) for 5-(25,10,4032) (# 6194) : der= 5-(25,9,1260) and res= 5-(25,10,4032) - the given design is the residual.

# 6196: 5-(24,9,1014)

clan: 11-(30,15,1014), 6 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6197: 5-(25,10,4056)

clan: 11-(30,15,1014), 1 times reduced t, 5 times derived
Tran van Trung construction (right) for 5-(24,9,1014) (# 6196) : der= 5-(24,9,1014) and res= 5-(24,10,3042) - the given design is the derived.

# 6198: 5-(24,9,102)

clan: 11-(30,15,102), 6 times derived
$PGL(2,23)$ (38 isomorphism types)

# 6199: 5-(25,10,408)

clan: 11-(30,15,102), 1 times reduced t, 5 times derived
Tran van Trung construction (right) for 5-(24,9,102) (# 6198) : der= 5-(24,9,102) and res= 5-(24,10,306) - the given design is the derived.
$PSL(2,23)+$ TvT construction 5-(24,9,102) $\cup$ 5-(24,10,306)

created: Fri Oct 23 11:10:14 CEST 2009