clan: 15-(32,16,10), 2 times reduced t, 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
supplementary design of 6-(24,8,63) (# 9846) with respect to smaller t
Tran van Trung construction (right) for 5-(23,7,90) (# 9849) : der= 5-(23,7,90) and res= 5-(23,8,480) - the given design is the derived.
Tran van Trung construction (left) for 5-(23,8,480) (# 9850) : der= 5-(23,7,90) and res= 5-(23,8,480) - the given design is the residual.
design 6-(24,8,90) (# 13371) with respect to smaller t

# 5827: 5-(24,8,571)

clan: 5-(24,8,571)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5828: 5-(24,8,572)

clan: 5-(24,8,572)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5829: 5-(24,8,573)

clan: 13-(32,16,573), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5830: 5-(24,8,574)

clan: 5-(24,8,574)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5831: 5-(24,8,575)

clan: 5-(24,8,575)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5832: 5-(24,8,576)

clan: 13-(32,16,576), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
$M_{12}\times id_2$

# 5833: 5-(24,8,577)

clan: 5-(24,8,577)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5834: 5-(24,8,578)

clan: 6-(25,8,102), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5835: 5-(24,8,579)

clan: 13-(32,16,579), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5836: 5-(24,8,58)

clan: 5-(24,8,58)
$PGL(2,23)$

# 5837: 5-(24,8,580)

clan: 5-(24,8,580)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5838: 5-(24,8,581)

clan: 5-(24,8,581)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5839: 5-(24,8,582)

clan: 13-(32,16,582), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5840: 5-(24,8,583)

clan: 5-(24,8,583)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5841: 5-(24,8,584)

clan: 5-(24,8,584)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5842: 5-(24,8,585)

clan: 13-(32,16,585), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,384) (# 10452)

# 5843: 5-(24,8,586)

clan: 5-(24,8,586)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5844: 5-(24,8,587)

clan: 5-(24,8,587)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5845: 5-(24,8,588)

clan: 13-(32,16,588), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5846: 5-(24,8,589)

clan: 6-(24,8,93), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5847: 5-(24,8,59)

clan: 5-(24,8,59)
$PGL(2,23)$

# 5848: 5-(24,8,590)

clan: 5-(24,8,590)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5849: 5-(24,8,591)

clan: 13-(32,16,591), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5850: 5-(24,8,592)

clan: 5-(24,8,592)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5851: 5-(24,8,593)

clan: 5-(24,8,593)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5852: 5-(24,8,594)

clan: 13-(32,16,594), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5853: 5-(24,8,595)

clan: 6-(25,8,105), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5854: 5-(24,8,596)

clan: 5-(24,8,596)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5855: 5-(24,8,597)

clan: 13-(32,16,597), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5856: 5-(24,8,598)

clan: 5-(24,8,598)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5857: 5-(24,8,599)

clan: 5-(24,8,599)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5858: 5-(24,8,6)

clan: 13-(32,16,6), 8 times derived
\cite{KramerMagliveras74}

# 5859: 5-(24,8,60)

clan: 13-(32,16,60), 8 times derived
$PGL(2,23)$

# 5860: 5-(24,8,600)

clan: 13-(32,16,600), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,369) (# 10449)

# 5861: 5-(24,8,601)

clan: 5-(24,8,601)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5862: 5-(24,8,602)

clan: 5-(24,8,602)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5863: 5-(24,8,603)

clan: 13-(32,16,603), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5864: 5-(24,8,604)

clan: 5-(24,8,604)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5865: 5-(24,8,605)

clan: 5-(24,8,605)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5866: 5-(24,8,606)

clan: 13-(32,16,606), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5867: 5-(24,8,607)

clan: 5-(24,8,607)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5868: 5-(24,8,608)

clan: 6-(24,8,96), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5869: 5-(24,8,609)

clan: 13-(32,16,609), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,360) (# 10446)

# 5870: 5-(24,8,61)

clan: 5-(24,8,61)
$PGL(2,23)$

# 5871: 5-(24,8,610)

clan: 5-(24,8,610)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5872: 5-(24,8,611)

clan: 5-(24,8,611)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5873: 5-(24,8,612)

clan: 17-(36,18,12), 10 times derived, 2 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
residual design of supplementary of 6-(25,8,63) (# 10405)
derived from supplementary of 6-(25,9,357) (# 13776)
residual design of 6-(25,8,108) (# 13778)
derived from 6-(25,9,612) (# 13779)

# 5874: 5-(24,8,613)

clan: 5-(24,8,613)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5875: 5-(24,8,614)

clan: 5-(24,8,614)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5876: 5-(24,8,615)

clan: 13-(32,16,615), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5877: 5-(24,8,616)

clan: 5-(24,8,616)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5878: 5-(24,8,617)

clan: 5-(24,8,617)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5879: 5-(24,8,618)

clan: 13-(32,16,618), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5880: 5-(24,8,619)

clan: 5-(24,8,619)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5881: 5-(24,8,62)

clan: 5-(24,8,62)
$PGL(2,23)$

# 5882: 5-(24,8,620)

clan: 5-(24,8,620)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5883: 5-(24,8,621)

clan: 13-(32,16,621), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5884: 5-(24,8,622)

clan: 5-(24,8,622)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5885: 5-(24,8,623)

clan: 5-(24,8,623)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5886: 5-(24,8,624)

clan: 13-(32,16,624), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5887: 5-(24,8,625)

clan: 5-(24,8,625)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5888: 5-(24,8,626)

clan: 5-(24,8,626)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5889: 5-(24,8,627)

clan: 15-(32,16,11), 2 times reduced t, 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
supplementary design of 6-(24,8,54) (# 9841) with respect to smaller t
Tran van Trung construction (right) for 5-(23,7,99) (# 9844) : der= 5-(23,7,99) and res= 5-(23,8,528) - the given design is the derived.
Tran van Trung construction (left) for 5-(23,8,528) (# 9845) : der= 5-(23,7,99) and res= 5-(23,8,528) - the given design is the residual.
design 6-(24,8,99) (# 13317) with respect to smaller t
derived from supplementary of 6-(25,9,342) (# 13325)
derived from 6-(25,9,627) (# 13327)