# 6400: 5-(26,11,17556)

- clan: 13-(30,15,44), 4 times reduced t, 4 times derived
- Tran van Trung construction (right) for 5-(25,10,5016) (# 6399) : der= 5-(25,10,5016) and res= 5-(25,11,12540) - the given design is the derived.

- clan: 13-(30,15,44), 5 times reduced t, 3 times derived
- Tran van Trung construction (right) for 5-(26,11,17556) (# 6400) : der= 5-(26,11,17556) and res= 5-(26,12,37620) - the given design is the derived.

- clan: 13-(30,15,44), 6 times reduced t, 2 times derived
- Tran van Trung construction (right) for 5-(27,12,55176) (# 6401) : der= 5-(27,12,55176) and res= 5-(27,13,103455) - the given design is the derived.

- clan: 13-(30,15,44), 7 times reduced t, 1 times derived
- Tran van Trung construction (right) for 5-(28,13,158631) (# 6402) : der= 5-(28,13,158631) and res= 5-(28,14,264385) - the given design is the derived.

- clan: 13-(30,15,44), 8 times reduced t
- Tran van Trung construction with complementary design for 5-(29,14,423016) (# 6403)

- clan: 11-(30,15,126), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,126), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,126) (# 6405) : der= 5-(24,9,126) and res= 5-(24,10,378) - the given design is the derived.

- clan: 13-(32,16,315), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,315), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1260) (# 6407) : der= 5-(24,8,315) and res= 5-(24,9,1260) - the given design is the residual.
- derived from 6-(26,10,1575) (# 10500)
- derived from supplementary of 6-(26,10,3270) (# 14009)

- clan: 13-(32,16,315), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1260) (# 6407) : der= 5-(24,9,1260) and res= 5-(24,10,3780) - the given design is the derived.
- residual design of 6-(26,10,1575) (# 10500)
- derived from 6-(26,11,5040) (# 14007)
- residual design of supplementary of 6-(26,10,3270) (# 14009)
- derived from supplementary of 6-(26,11,10464) (# 14010)

- clan: 13-(32,16,315), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1575) (# 6408) : der= 5-(25,9,1575) and res= 5-(25,10,5040) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5040) (# 6409) : der= 5-(25,9,1575) and res= 5-(25,10,5040) - the given design is the residual.
- design 6-(26,10,1575) (# 10500) with respect to smaller t
- derived from 6-(27,11,6615) (# 10675)
- derived from supplementary of 6-(27,11,13734) (# 14008)
- supplementary design of 6-(26,10,3270) (# 14009) with respect to smaller t

- clan: 11-(30,15,1266), 6 times derived
- $M_{11,12}\times id_2$
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1266), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1266) (# 6411) : der= 5-(24,9,1266) and res= 5-(24,10,3798) - the given design is the derived.

- clan: 13-(32,16,318), 7 times derived, 1 times residual
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 13-(32,16,318), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1272) (# 6413) : der= 5-(24,8,318) and res= 5-(24,9,1272) - the given design is the residual.

- clan: 13-(32,16,318), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1272) (# 6413) : der= 5-(24,9,1272) and res= 5-(24,10,3816) - the given design is the derived.

- clan: 13-(32,16,318), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1590) (# 6414) : der= 5-(25,9,1590) and res= 5-(25,10,5088) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5088) (# 6415) : der= 5-(25,9,1590) and res= 5-(25,10,5088) - the given design is the residual.

- clan: 11-(30,15,1278), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1278), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1278) (# 6417) : der= 5-(24,9,1278) and res= 5-(24,10,3834) - the given design is the derived.

- clan: 13-(32,16,321), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,321), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1284) (# 6419) : der= 5-(24,8,321) and res= 5-(24,9,1284) - the given design is the residual.
- derived from 6-(26,10,1605) (# 14014)
- derived from supplementary of 6-(26,10,3240) (# 14017)

- clan: 13-(32,16,321), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1284) (# 6419) : der= 5-(24,9,1284) and res= 5-(24,10,3852) - the given design is the derived.
- residual design of 6-(26,10,1605) (# 14014)
- derived from 6-(26,11,5136) (# 14015)
- residual design of supplementary of 6-(26,10,3240) (# 14017)
- derived from supplementary of 6-(26,11,10368) (# 14018)

- clan: 13-(32,16,321), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1605) (# 6420) : der= 5-(25,9,1605) and res= 5-(25,10,5136) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5136) (# 6421) : der= 5-(25,9,1605) and res= 5-(25,10,5136) - the given design is the residual.
- derived from 6-(27,11,6741) (# 10680)
- design 6-(26,10,1605) (# 14014) with respect to smaller t
- derived from supplementary of 6-(27,11,13608) (# 14016)
- supplementary design of 6-(26,10,3240) (# 14017) with respect to smaller t

- clan: 11-(30,15,1290), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1290), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1290) (# 6423) : der= 5-(24,9,1290) and res= 5-(24,10,3870) - the given design is the derived.

- clan: 13-(32,16,324), 7 times derived, 1 times residual
- $M_{11,12}\times id_2$
- $PGL(2,23)$ (>1 isomorphism types)
- residual design of 6-(25,9,324) (# 10443)
- derived from 6-(25,10,1296) (# 17560)
- derived from supplementary of 6-(25,10,2580) (# 17562)

- clan: 13-(32,16,324), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1296) (# 6425) : der= 5-(24,8,324) and res= 5-(24,9,1296) - the given design is the residual.
- design 6-(25,9,324) (# 10443) with respect to smaller t
- derived from 6-(26,10,1620) (# 10504)
- derived from supplementary of 6-(26,10,3225) (# 14026)

- clan: 13-(32,16,324), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1296) (# 6425) : der= 5-(24,9,1296) and res= 5-(24,10,3888) - the given design is the derived.
- residual design of 6-(26,10,1620) (# 10504)
- derived from 6-(26,11,5184) (# 14024)
- residual design of supplementary of 6-(26,10,3225) (# 14026)
- derived from supplementary of 6-(26,11,10320) (# 14027)
- design 6-(25,10,1296) (# 17560) with respect to smaller t
- supplementary design of 6-(25,10,2580) (# 17562) with respect to smaller t

- clan: 13-(32,16,324), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1620) (# 6426) : der= 5-(25,9,1620) and res= 5-(25,10,5184) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5184) (# 6427) : der= 5-(25,9,1620) and res= 5-(25,10,5184) - the given design is the residual.
- design 6-(26,10,1620) (# 10504) with respect to smaller t
- derived from 6-(27,11,6804) (# 10686)
- derived from supplementary of 6-(27,11,13545) (# 14025)
- supplementary design of 6-(26,10,3225) (# 14026) with respect to smaller t

- clan: 11-(30,15,1302), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1302), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1302) (# 6429) : der= 5-(24,9,1302) and res= 5-(24,10,3906) - the given design is the derived.

- clan: 11-(30,15,1302), 2 times reduced t, 4 times derived
- Tran van Trung construction (right) for 5-(25,10,5208) (# 6430) : der= 5-(25,10,5208) and res= 5-(25,11,13020) - the given design is the derived.

- clan: 11-(30,15,1302), 3 times reduced t, 3 times derived
- Tran van Trung construction (right) for 5-(26,11,18228) (# 6431) : der= 5-(26,11,18228) and res= 5-(26,12,39060) - the given design is the derived.

- clan: 11-(30,15,1302), 4 times reduced t, 2 times derived
- Tran van Trung construction (right) for 5-(27,12,57288) (# 6432) : der= 5-(27,12,57288) and res= 5-(27,13,107415) - the given design is the derived.

- clan: 11-(30,15,1302), 5 times reduced t, 1 times derived
- Tran van Trung construction (right) for 5-(28,13,164703) (# 6433) : der= 5-(28,13,164703) and res= 5-(28,14,274505) - the given design is the derived.

- clan: 11-(30,15,1302), 6 times reduced t
- Tran van Trung construction with complementary design for 5-(29,14,439208) (# 6434)

- clan: 13-(32,16,327), 7 times derived, 1 times residual
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 13-(32,16,327), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1308) (# 6436) : der= 5-(24,8,327) and res= 5-(24,9,1308) - the given design is the residual.

- clan: 13-(32,16,327), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1308) (# 6436) : der= 5-(24,9,1308) and res= 5-(24,10,3924) - the given design is the derived.

- clan: 13-(32,16,327), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1635) (# 6437) : der= 5-(25,9,1635) and res= 5-(25,10,5232) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5232) (# 6438) : der= 5-(25,9,1635) and res= 5-(25,10,5232) - the given design is the residual.

- clan: 11-(30,15,1314), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1314), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1314) (# 6440) : der= 5-(24,9,1314) and res= 5-(24,10,3942) - the given design is the derived.

- clan: 13-(32,16,33), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,33), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,132) (# 6442) : der= 5-(24,8,33) and res= 5-(24,9,132) - the given design is the residual.

- clan: 13-(32,16,33), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,132) (# 6442) : der= 5-(24,9,132) and res= 5-(24,10,396) - the given design is the derived.

- clan: 13-(32,16,33), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,165) (# 6443) : der= 5-(25,9,165) and res= 5-(25,10,528) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,528) (# 6444) : der= 5-(25,9,165) and res= 5-(25,10,528) - the given design is the residual.

- clan: 13-(32,16,33), 2 times reduced t, 5 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(25,10,528) (# 6444) : der= 5-(25,10,528) and res= 5-(25,11,1320) - the given design is the derived.

- clan: 13-(32,16,33), 3 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(26,10,693) (# 6445) : der= 5-(26,10,693) and res= 5-(26,11,1848) - the given design is the derived.
- Tran van Trung construction (left) for 5-(26,11,1848) (# 6446) : der= 5-(26,10,693) and res= 5-(26,11,1848) - the given design is the residual.

- clan: 13-(32,16,33), 3 times reduced t, 4 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(26,11,1848) (# 6446) : der= 5-(26,11,1848) and res= 5-(26,12,3960) - the given design is the derived.

- clan: 13-(32,16,33), 4 times reduced t, 4 times derived
- Tran van Trung construction (right) for 5-(27,11,2541) (# 6447) : der= 5-(27,11,2541) and res= 5-(27,12,5808) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,12,5808) (# 6448) : der= 5-(27,11,2541) and res= 5-(27,12,5808) - the given design is the residual.

- clan: 13-(32,16,33), 4 times reduced t, 3 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(27,12,5808) (# 6448) : der= 5-(27,12,5808) and res= 5-(27,13,10890) - the given design is the derived.

- clan: 13-(32,16,33), 5 times reduced t, 3 times derived
- Tran van Trung construction (right) for 5-(28,12,8349) (# 6449) : der= 5-(28,12,8349) and res= 5-(28,13,16698) - the given design is the derived.
- Tran van Trung construction (left) for 5-(28,13,16698) (# 6450) : der= 5-(28,12,8349) and res= 5-(28,13,16698) - the given design is the residual.

- clan: 13-(32,16,33), 5 times reduced t, 2 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(28,13,16698) (# 6450) : der= 5-(28,13,16698) and res= 5-(28,14,27830) - the given design is the derived.

- clan: 13-(32,16,33), 6 times reduced t, 2 times derived
- Tran van Trung construction (right) for 5-(29,13,25047) (# 6451) : der= 5-(29,13,25047) and res= 5-(29,14,44528) - the given design is the derived.
- Tran van Trung construction (left) for 5-(29,14,44528) (# 6452) : der= 5-(29,13,25047) and res= 5-(29,14,44528) - the given design is the residual.

- clan: 13-(32,16,33), 6 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction with complementary design for 5-(29,14,44528) (# 6452)

- clan: 13-(32,16,33), 7 times reduced t, 1 times derived
- Tran van Trung construction (right) for 5-(30,14,69575) (# 6453) : der= 5-(30,14,69575) and res= 5-(30,15,111320) - the given design is the derived.
- Tran van Trung construction (left) for 5-(30,15,111320) (# 6454) : der= 5-(30,14,69575) and res= 5-(30,15,111320) - the given design is the residual.

- clan: 13-(32,16,33), 8 times reduced t
- Tran van Trung construction with complementary design for 5-(31,15,180895) (# 6455)

- clan: 13-(32,16,330), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,330), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1320) (# 6457) : der= 5-(24,8,330) and res= 5-(24,9,1320) - the given design is the residual.
- derived from 6-(26,10,1650) (# 10507)
- derived from supplementary of 6-(26,10,3195) (# 14034)

- clan: 13-(32,16,330), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1320) (# 6457) : der= 5-(24,9,1320) and res= 5-(24,10,3960) - the given design is the derived.
- residual design of 6-(26,10,1650) (# 10507)
- derived from 6-(26,11,5280) (# 14032)
- residual design of supplementary of 6-(26,10,3195) (# 14034)
- derived from supplementary of 6-(26,11,10224) (# 14035)

- clan: 13-(32,16,330), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1650) (# 6458) : der= 5-(25,9,1650) and res= 5-(25,10,5280) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5280) (# 6459) : der= 5-(25,9,1650) and res= 5-(25,10,5280) - the given design is the residual.
- design 6-(26,10,1650) (# 10507) with respect to smaller t
- derived from 6-(27,11,6930) (# 14031)
- derived from supplementary of 6-(27,11,13419) (# 14033)
- supplementary design of 6-(26,10,3195) (# 14034) with respect to smaller t

- clan: 13-(32,16,330), 2 times reduced t, 5 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(25,10,5280) (# 6459) : der= 5-(25,10,5280) and res= 5-(25,11,13200) - the given design is the derived.
- residual design of 6-(27,11,6930) (# 14031)
- design 6-(26,11,5280) (# 14032) with respect to smaller t
- residual design of supplementary of 6-(27,11,13419) (# 14033)
- supplementary design of 6-(26,11,10224) (# 14035) with respect to smaller t

- clan: 13-(32,16,330), 3 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(26,10,6930) (# 6460) : der= 5-(26,10,6930) and res= 5-(26,11,18480) - the given design is the derived.
- Tran van Trung construction (left) for 5-(26,11,18480) (# 6461) : der= 5-(26,10,6930) and res= 5-(26,11,18480) - the given design is the residual.
- design 6-(27,11,6930) (# 14031) with respect to smaller t
- supplementary design of 6-(27,11,13419) (# 14033) with respect to smaller t

- clan: 13-(32,16,330), 3 times reduced t, 4 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(26,11,18480) (# 6461) : der= 5-(26,11,18480) and res= 5-(26,12,39600) - the given design is the derived.

- clan: 13-(32,16,330), 4 times reduced t, 4 times derived
- Tran van Trung construction (right) for 5-(27,11,25410) (# 6462) : der= 5-(27,11,25410) and res= 5-(27,12,58080) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,12,58080) (# 6463) : der= 5-(27,11,25410) and res= 5-(27,12,58080) - the given design is the residual.

- clan: 13-(32,16,330), 4 times reduced t, 3 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(27,12,58080) (# 6463) : der= 5-(27,12,58080) and res= 5-(27,13,108900) - the given design is the derived.

- clan: 13-(32,16,330), 5 times reduced t, 3 times derived
- Tran van Trung construction (right) for 5-(28,12,83490) (# 6464) : der= 5-(28,12,83490) and res= 5-(28,13,166980) - the given design is the derived.
- Tran van Trung construction (left) for 5-(28,13,166980) (# 6465) : der= 5-(28,12,83490) and res= 5-(28,13,166980) - the given design is the residual.

- clan: 13-(32,16,330), 5 times reduced t, 2 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(28,13,166980) (# 6465) : der= 5-(28,13,166980) and res= 5-(28,14,278300) - the given design is the derived.

- clan: 13-(32,16,330), 6 times reduced t, 2 times derived
- Tran van Trung construction (right) for 5-(29,13,250470) (# 6466) : der= 5-(29,13,250470) and res= 5-(29,14,445280) - the given design is the derived.
- Tran van Trung construction (left) for 5-(29,14,445280) (# 6467) : der= 5-(29,13,250470) and res= 5-(29,14,445280) - the given design is the residual.

- clan: 13-(32,16,330), 6 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction with complementary design for 5-(29,14,445280) (# 6467)

- clan: 13-(32,16,330), 7 times reduced t, 1 times derived
- Tran van Trung construction (right) for 5-(30,14,695750) (# 6468) : der= 5-(30,14,695750) and res= 5-(30,15,1113200) - the given design is the derived.
- Tran van Trung construction (left) for 5-(30,15,1113200) (# 6469) : der= 5-(30,14,695750) and res= 5-(30,15,1113200) - the given design is the residual.

- clan: 13-(32,16,330), 8 times reduced t
- Tran van Trung construction with complementary design for 5-(31,15,1808950) (# 6470)

- clan: 11-(30,15,1326), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1326), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1326) (# 6472) : der= 5-(24,9,1326) and res= 5-(24,10,3978) - the given design is the derived.

- clan: 13-(32,16,333), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,333), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1332) (# 6474) : der= 5-(24,8,333) and res= 5-(24,9,1332) - the given design is the residual.

- clan: 13-(32,16,333), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1332) (# 6474) : der= 5-(24,9,1332) and res= 5-(24,10,3996) - the given design is the derived.

- clan: 13-(32,16,333), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1665) (# 6475) : der= 5-(25,9,1665) and res= 5-(25,10,5328) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5328) (# 6476) : der= 5-(25,9,1665) and res= 5-(25,10,5328) - the given design is the residual.

- clan: 11-(30,15,1338), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1338), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1338) (# 6478) : der= 5-(24,9,1338) and res= 5-(24,10,4014) - the given design is the derived.

- clan: 13-(32,16,336), 7 times derived, 1 times residual
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 13-(32,16,336), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1344) (# 6480) : der= 5-(24,8,336) and res= 5-(24,9,1344) - the given design is the residual.

- clan: 13-(32,16,336), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1344) (# 6480) : der= 5-(24,9,1344) and res= 5-(24,10,4032) - the given design is the derived.

- clan: 13-(32,16,336), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1680) (# 6481) : der= 5-(25,9,1680) and res= 5-(25,10,5376) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5376) (# 6482) : der= 5-(25,9,1680) and res= 5-(25,10,5376) - the given design is the residual.

- clan: 11-(30,15,1350), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1350), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1350) (# 6484) : der= 5-(24,9,1350) and res= 5-(24,10,4050) - the given design is the derived.

- clan: 13-(32,16,339), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)
- derived from 6-(25,10,1356) (# 13574)
- derived from supplementary of 6-(25,10,2520) (# 13577)

- clan: 13-(32,16,339), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1356) (# 6486) : der= 5-(24,8,339) and res= 5-(24,9,1356) - the given design is the residual.
- derived from 6-(26,10,1695) (# 10511)

- clan: 13-(32,16,339), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1356) (# 6486) : der= 5-(24,9,1356) and res= 5-(24,10,4068) - the given design is the derived.
- residual design of 6-(26,10,1695) (# 10511)
- derived from 6-(26,11,5424) (# 13573)
- design 6-(25,10,1356) (# 13574) with respect to smaller t
- derived from supplementary of 6-(26,11,10080) (# 13576)
- supplementary design of 6-(25,10,2520) (# 13577) with respect to smaller t

- clan: 13-(32,16,339), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1695) (# 6487) : der= 5-(25,9,1695) and res= 5-(25,10,5424) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5424) (# 6488) : der= 5-(25,9,1695) and res= 5-(25,10,5424) - the given design is the residual.
- design 6-(26,10,1695) (# 10511) with respect to smaller t
- derived from 6-(27,11,7119) (# 13583)

- clan: 11-(30,15,1362), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1362), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1362) (# 6490) : der= 5-(24,9,1362) and res= 5-(24,10,4086) - the given design is the derived.

- clan: 15-(32,16,6), 2 times reduced t, 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)
- Tran van Trung construction (right) for 5-(23,8,288) (# 9843) : der= 5-(23,8,288) and res= 5-(23,9,1080) - the given design is the derived.
- design 6-(24,9,288) (# 13323) with respect to smaller t
- supplementary design of 6-(24,9,528) (# 13324) with respect to smaller t
- residual design of 6-(25,9,342) (# 13325)
- derived from 6-(25,10,1368) (# 13326)
- residual design of supplementary of 6-(25,9,627) (# 13327)
- derived from supplementary of 6-(25,10,2508) (# 13328)

- clan: 15-(32,16,6), 3 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1368) (# 6492) : der= 5-(24,8,342) and res= 5-(24,9,1368) - the given design is the residual.
- design 6-(25,9,342) (# 13325) with respect to smaller t
- supplementary design of 6-(25,9,627) (# 13327) with respect to smaller t
- derived from 6-(26,10,1710) (# 13329)
- derived from supplementary of 6-(26,10,3135) (# 13331)

- clan: 15-(32,16,6), 3 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1368) (# 6492) : der= 5-(24,9,1368) and res= 5-(24,10,4104) - the given design is the derived.
- design 6-(25,10,1368) (# 13326) with respect to smaller t
- supplementary design of 6-(25,10,2508) (# 13328) with respect to smaller t
- residual design of 6-(26,10,1710) (# 13329)
- derived from 6-(26,11,5472) (# 13330)
- residual design of supplementary of 6-(26,10,3135) (# 13331)
- derived from supplementary of 6-(26,11,10032) (# 13332)

- clan: 15-(32,16,6), 4 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,1710) (# 6493) : der= 5-(25,9,1710) and res= 5-(25,10,5472) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,5472) (# 6494) : der= 5-(25,9,1710) and res= 5-(25,10,5472) - the given design is the residual.
- derived from 6-(27,11,7182) (# 10691)
- design 6-(26,10,1710) (# 13329) with respect to smaller t
- supplementary design of 6-(26,10,3135) (# 13331) with respect to smaller t
- derived from supplementary of 6-(27,11,13167) (# 13334)

- clan: 15-(32,16,6), 4 times reduced t, 5 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(25,10,5472) (# 6494) : der= 5-(25,10,5472) and res= 5-(25,11,13680) - the given design is the derived.
- residual design of 6-(27,11,7182) (# 10691)
- design 6-(26,11,5472) (# 13330) with respect to smaller t
- supplementary design of 6-(26,11,10032) (# 13332) with respect to smaller t
- derived from 6-(27,12,19152) (# 13333)
- residual design of supplementary of 6-(27,11,13167) (# 13334)
- derived from supplementary of 6-(27,12,35112) (# 13335)

- clan: 15-(32,16,6), 5 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(26,10,7182) (# 6495) : der= 5-(26,10,7182) and res= 5-(26,11,19152) - the given design is the derived.
- Tran van Trung construction (left) for 5-(26,11,19152) (# 6496) : der= 5-(26,10,7182) and res= 5-(26,11,19152) - the given design is the residual.
- design 6-(27,11,7182) (# 10691) with respect to smaller t
- supplementary design of 6-(27,11,13167) (# 13334) with respect to smaller t
- derived from 6-(28,12,26334) (# 13336)
- derived from supplementary of 6-(28,12,48279) (# 13338)

- clan: 15-(32,16,6), 5 times reduced t, 4 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(26,11,19152) (# 6496) : der= 5-(26,11,19152) and res= 5-(26,12,41040) - the given design is the derived.
- design 6-(27,12,19152) (# 13333) with respect to smaller t
- supplementary design of 6-(27,12,35112) (# 13335) with respect to smaller t
- residual design of 6-(28,12,26334) (# 13336)
- derived from 6-(28,13,60192) (# 13337)
- residual design of supplementary of 6-(28,12,48279) (# 13338)
- derived from supplementary of 6-(28,13,110352) (# 13339)

- clan: 15-(32,16,6), 6 times reduced t, 4 times derived
- Tran van Trung construction (right) for 5-(27,11,26334) (# 6497) : der= 5-(27,11,26334) and res= 5-(27,12,60192) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,12,60192) (# 6498) : der= 5-(27,11,26334) and res= 5-(27,12,60192) - the given design is the residual.
- design 6-(28,12,26334) (# 13336) with respect to smaller t
- supplementary design of 6-(28,12,48279) (# 13338) with respect to smaller t
- derived from 6-(29,13,86526) (# 13340)
- derived from supplementary of 6-(29,13,158631) (# 13342)

created: Fri Oct 23 11:10:18 CEST 2009