t designs with small t, id ge 8500

# 8500: 5-(32,8,1430)

clan: 5-(32,8,1430)
$PSL(2,31)$

# 8501: 5-(32,8,1435)

clan: 5-(32,8,1435)
$PSL(2,31)$

# 8502: 5-(32,8,1440)

clan: 10-(36,12,160), 1 times reduced t, 4 times derived
$PSL(2,31)$
derived from 6-(33,9,1440) (# 12518)
design 6-(32,8,160) (# 16272) with respect to smaller t
derived from supplementary of 6-(33,9,1485) (# 16274)
supplementary design of 6-(32,8,165) (# 16275) with respect to smaller t
Tran van Trung construction (right) for 5-(31,7,160) (# 16277) : der= 5-(31,7,160) and res= 5-(31,8,1280) - the given design is the derived.
Tran van Trung construction (left) for 5-(31,8,1280) (# 16278) : der= 5-(31,7,160) and res= 5-(31,8,1280) - the given design is the residual.

# 8503: 5-(32,8,1445)

clan: 5-(32,8,1445)
$AGL(4,2)\times C_2$

# 8504: 5-(32,8,1450)

clan: 6-(33,8,174), 1 times residual
$S4 \times PSL(2,7)$

# 8505: 5-(32,8,1455)

clan: 9-(36,12,1455), 4 times derived
$PSL(2,31)$

# 8506: 5-(32,8,1460)

clan: 5-(32,8,1460)
$PSL(2,31)$

# 8507: 5-(33,6,4)

clan: 5-(33,6,4)
$PGL(2,32)$ 39970 solutions

# 8508: 5-(33,6,8)

clan: 5-(33,6,8)
$PGL(2,32)$ 15382765 solutions

# 8509: 5-(33,6,12)

clan: 5-(33,6,12)
\cite{Sebille98} $P\Gamma L(2,32)$

# 8510: 5-(33,7,42)

clan: 7-(34,8,3), 1 times reduced t, 1 times derived
\cite{Sebille98} $P\Gamma L(2,32)$

# 8511: 5-(34,6,5)

clan: 27-(56,28,5), 22 times derived
\cite{Sebille98} $P\Gamma L(2,16)\times C_2$ 15 solutions, $PGL(2,16)\times C_2$ more than 250000000 solutions
$P\Gamma L(2,32)+$ 6 solutions
$P\Gamma L(2,16)\times C_2$ 23 solutions

# 8512: 5-(34,6,4)

clan: 27-(56,28,4), 22 times derived
$PGL(2,32)+$ 21945 solutions

# 8513: 5-(34,6,9)

clan: 27-(56,28,9), 22 times derived
$P\Gamma L(2,32)+$ 8 solutions
derived from 6-(35,7,9) (# 12843)

# 8514: 5-(34,6,12)

clan: 27-(56,28,12), 22 times derived
\cite{Sebille98} $P\Gamma L(2,16)\times C_2$ 5304 solutions
$PGL(2,16)\times Id_2$ > 8000000000 solutions

# 8515: 5-(34,7,196)

clan: 27-(56,28,14), 21 times derived, 1 times residual
$PGL(2,16)\times C_2$

# 8516: 5-(34,7,210)

clan: 27-(56,28,15), 21 times derived, 1 times residual
$PGL(2,16)\times C_2$

# 8517: 5-(34,7,70)

clan: 27-(56,28,5), 21 times derived, 1 times residual
\cite{Sebille98} $P\Gamma L(2,16)\times C_2$
derived from 6-(35,8,70) (# 12849)

# 8518: 5-(35,7,75)

clan: 27-(56,28,5), 1 times reduced t, 21 times derived
Tran van Trung construction (left) for 5-(34,7,70) (# 8517) : der= 5-(34,6,5) and res= 5-(34,7,70) - the given design is the residual.

# 8519: 5-(36,6,1)

clan: 29-(60,30,1), 24 times derived
\cite{Bettenetal98a} $PGL(2,17)\times C_2$

# 8520: 5-(36,6,10)

clan: 29-(60,30,10), 24 times derived
$PGL(2,17)\times C_2$

# 8521: 5-(36,6,11)

clan: 29-(60,30,11), 24 times derived
$PGL(2,17)\times C_2$

# 8522: 5-(36,6,12)

clan: 29-(60,30,12), 24 times derived
$PGL(2,17)\times C_2$

# 8523: 5-(36,6,14)

clan: 29-(60,30,14), 24 times derived
$PGL(2,17)\times C_2$

# 8524: 5-(36,6,15)

clan: 29-(60,30,15), 24 times derived
$PGL(2,17)\times C_2$

# 8525: 5-(36,6,16)

clan: 29-(60,30,16), 24 times derived
$PGL(2,17)\times C_2$

# 8526: 5-(36,6,2)

clan: 29-(60,30,2), 24 times derived
$PGL(2,17)\times C_2$

# 8527: 5-(36,6,3)

clan: 29-(60,30,3), 24 times derived
$PGL(2,17)\times C_2$

# 8528: 5-(36,6,4)

clan: 29-(60,30,4), 24 times derived
$PGL(2,17)\times C_2$

# 8529: 5-(36,6,5)

clan: 29-(60,30,5), 24 times derived
$PGL(2,17)\times C_2$

# 8530: 5-(36,6,6)

clan: 29-(60,30,6), 24 times derived
$PGL(2,17)\times C_2$

# 8531: 5-(36,6,7)

clan: 29-(60,30,7), 24 times derived
$PGL(2,17)\times C_2$

# 8532: 5-(36,6,8)

clan: 29-(60,30,8), 24 times derived
$PGL(2,17)\times C_2$

# 8533: 5-(36,6,9)

clan: 29-(60,30,9), 24 times derived
$PGL(2,17)\times C_2$

# 8534: 5-(36,7,165)

clan: 29-(60,30,11), 23 times derived, 1 times residual
$S_9^{[2]}$ (>=1 isom. types)

# 8535: 5-(37,7,176)

clan: 29-(60,30,11), 1 times reduced t, 23 times derived
Tran van Trung construction (left) for 5-(36,7,165) (# 8534) : der= 5-(36,6,11) and res= 5-(36,7,165) - the given design is the residual.

# 8536: 5-(38,6,12)

clan: 9-(42,10,12), 4 times derived
\cite{Sebille98} $PGL(2,37)$

# 8537: 5-(38,6,9)

clan: 9-(42,10,9), 4 times derived
\cite{Sebille98} $PGL(2,37)$

# 8538: 5-(38,7,198)

clan: 6-(38,7,12), 1 times reduced t
$PGL(2,37)$

# 8539: 5-(38,7,264)

clan: 30-(62,31,16), 1 times reduced t, 24 times derived
$PGL(2,37)$ halving
design 6-(38,7,16) (# 12900) with respect to smaller t
supplementary design of 6-(38,7,16) (# 12900) with respect to smaller t
Tran van Trung construction (right) for 5-(37,6,16) (# 12901) : der= 5-(37,6,16) and res= 5-(37,7,248) - the given design is the derived.
Tran van Trung construction (left) for 5-(37,7,248) (# 12902) : der= 5-(37,6,16) and res= 5-(37,7,248) - the given design is the residual.
derived from 6-(39,8,264) (# 12906)
derived from supplementary of 6-(39,8,264) (# 12906)

# 8540: 5-(39,6,16)

clan: 15-(49,16,16), 10 times derived
$PSL(3,3) \times C_3$

# 8541: 5-(42,6,13)

clan: 35-(72,36,13), 30 times derived
$PGL(2,13)\times S_3$

# 8542: 5-(42,7,306)

clan: 35-(72,36,17), 29 times derived, 1 times residual
$PSL(3,4) \times C_2$ 3 solutions

# 8543: 5-(46,8,1060)

clan: 9-(50,12,1060), 4 times derived
$M_{23}\times Id_2$

# 8544: 5-(46,8,1120)

clan: 9-(50,12,1120), 4 times derived
$M_{23}\times Id_2$

# 8545: 5-(46,8,1220)

clan: 9-(50,12,1220), 4 times derived
$M_{23}\times Id_2$

# 8546: 5-(46,8,1280)

clan: 9-(50,12,1280), 4 times derived
$M_{23}\times Id_2$

# 8547: 5-(46,8,1380)

clan: 9-(50,12,1380), 4 times derived
$M_{23}\times Id_2$

# 8548: 5-(46,8,1440)

clan: 9-(50,12,1440), 4 times derived
$M_{23}\times Id_2$

# 8549: 5-(46,8,3840)

clan: 9-(50,12,3840), 4 times derived
$M_{23}\times Id_2$

# 8550: 5-(46,8,4160)

clan: 39-(80,40,16), 32 times derived, 2 times residual
$M_{23}\times Id_2$

# 8551: 5-(46,8,4580)

clan: 9-(50,12,4580), 4 times derived
$M_{23}\times Id_2$

# 8552: 5-(46,8,5380)

clan: 9-(50,12,5380), 4 times derived
$M_{23}\times Id_2$

# 8553: 5-(46,8,800)

clan: 9-(50,12,800), 4 times derived
$M_{23}\times Id_2$ 2 solutions

# 8554: 5-(46,8,900)

clan: 9-(50,12,900), 4 times derived
$M_{23}\times Id_2$ 2 solutions

# 8555: 5-(46,8,960)

clan: 9-(50,12,960), 4 times derived
$M_{23}\times Id_2$

# 8556: 5-(48,6,1)

clan: 41-(84,42,1), 36 times derived
\cite{Denniston76} \cite{Grannelletal93} $PSL(2,47)$ (459 isom. types)

# 8557: 5-(48,6,13)

clan: 41-(84,42,13), 36 times derived
$PSL(2,47)$

# 8558: 5-(48,6,17)

clan: 41-(84,42,17), 36 times derived
$PSL(2,47)$

# 8559: 5-(48,6,18)

clan: 41-(84,42,18), 36 times derived
$PSL(2,47)$

# 8560: 5-(48,6,2)

clan: 41-(84,42,2), 36 times derived
$PGL(2,23)\times C_2$, $PSL(2,47)$

# 8561: 5-(48,6,20)

clan: 41-(84,42,20), 36 times derived
$PGL(2,23)\times C_2$

# 8562: 5-(48,6,21)

clan: 41-(84,42,21), 36 times derived
$PSL(2,47)$

# 8563: 5-(48,6,3)

clan: 41-(84,42,3), 36 times derived
$PGL(2,23)\times C_2$, $PSL(2,47)$

# 8564: 5-(48,6,4)

clan: 41-(84,42,4), 36 times derived
$PGL(2,23)\times C_2$, $PSL(2,47)$

# 8565: 5-(48,6,5)

clan: 41-(84,42,5), 36 times derived
$PGL(2,23)\times C_2$, $PSL(2,47)$

# 8566: 5-(48,6,6)

clan: 41-(84,42,6), 36 times derived
$PGL(2,23)\times C_2$, $PSL(2,47)$

# 8567: 5-(48,6,7)

clan: 41-(84,42,7), 36 times derived
$PGL(2,23)\times C_2$, $PSL(2,47)$

# 8568: 5-(48,6,8)

clan: 41-(84,42,8), 36 times derived
$PSL(2,47)$

# 8569: 5-(48,7,273)

clan: 41-(84,42,13), 35 times derived, 1 times residual
$PSL(2,47)$

# 8570: 5-(49,7,286)

clan: 41-(84,42,13), 1 times reduced t, 35 times derived
Tran van Trung construction (left) for 5-(48,7,273) (# 8569) : der= 5-(48,6,13) and res= 5-(48,7,273) - the given design is the residual.

# 8571: 5-(49,7,294)