# 11900: 5-(31,15,2220075)

- clan: 13-(32,16,405), 7 times reduced t, 1 times derived
- Tran van Trung construction (left) for 5-(30,15,1366200) (# 11896) : der= 5-(30,14,853875) and res= 5-(30,15,1366200) - the given design is the residual.
- Tran van Trung construction (right) for 5-(30,14,853875) (# 11897) : der= 5-(30,14,853875) and res= 5-(30,15,1366200) - the given design is the derived.
- design 6-(31,15,853875) (# 15439) with respect to smaller t
- supplementary design of 6-(31,15,1189100) (# 15443) with respect to smaller t
- derived from 6-(32,16,2220075) (# 15444)
- derived from supplementary of 6-(32,16,3091660) (# 15448)

- clan: 13-(32,16,564), 7 times reduced t, 1 times derived
- Tran van Trung construction (left) for 5-(30,15,1902560) (# 11898) : der= 5-(30,14,1189100) and res= 5-(30,15,1902560) - the given design is the residual.
- Tran van Trung construction (right) for 5-(30,14,1189100) (# 11899) : der= 5-(30,14,1189100) and res= 5-(30,15,1902560) - the given design is the derived.
- supplementary design of 6-(31,15,853875) (# 15439) with respect to smaller t
- design 6-(31,15,1189100) (# 15443) with respect to smaller t
- derived from supplementary of 6-(32,16,2220075) (# 15444)
- derived from 6-(32,16,3091660) (# 15448)

- clan: 13-(32,16,405), 8 times reduced t
- Tran van Trung construction with complementary design for 5-(31,15,2220075) (# 11900)
- design 6-(32,16,2220075) (# 15444) with respect to smaller t
- supplementary design of 6-(32,16,3091660) (# 15448) with respect to smaller t
- Tran van Trung construction (left) for 5-(31,16,3229200) (# 15450) : der= 5-(31,15,2220075) and res= 5-(31,16,3229200) - the given design is the residual.

- clan: 13-(32,16,564), 8 times reduced t
- Tran van Trung construction with complementary design for 5-(31,15,3091660) (# 11901)
- supplementary design of 6-(32,16,2220075) (# 15444) with respect to smaller t
- design 6-(32,16,3091660) (# 15448) with respect to smaller t
- Tran van Trung construction (left) for 5-(31,16,4496960) (# 15451) : der= 5-(31,15,3091660) and res= 5-(31,16,4496960) - the given design is the residual.

- clan: 13-(32,16,450), 3 times reduced t, 3 times derived, 1 times residual
- $Sp(6,2)$
- design 7-(28,13,25200) (# 15460) with respect to smaller t
- Tran van Trung construction (right) for 6-(27,12,25200) (# 15461) : der= 6-(27,12,25200) and res= 6-(27,13,54000) - the given design is the derived.
- Tran van Trung construction (left) for 6-(27,13,54000) (# 15462) : der= 6-(27,12,25200) and res= 6-(27,13,54000) - the given design is the residual.
- derived from 7-(29,14,79200) (# 15482)

- clan: 13-(32,16,450), 4 times reduced t, 3 times derived, 1 times residual
- design 6-(28,13,79200) (# 11904) with respect to smaller t
- Tran van Trung construction (right) for 5-(27,12,79200) (# 11906) : der= 5-(27,12,79200) and res= 5-(27,13,148500) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,13,148500) (# 11907) : der= 5-(27,12,79200) and res= 5-(27,13,148500) - the given design is the residual.
- supplementary design of 6-(28,13,91344) (# 15463) with respect to smaller t
- residual design of 6-(29,13,113850) (# 15476)
- derived from 6-(29,14,227700) (# 15479)
- residual design of supplementary of 6-(29,13,131307) (# 15483)
- derived from supplementary of 6-(29,14,262614) (# 15484)

- clan: 13-(32,16,450), 3 times reduced t, 4 times derived, 1 times residual
- derived from 6-(28,13,79200) (# 11904)
- design 6-(27,12,25200) (# 15461) with respect to smaller t
- derived from supplementary of 6-(28,13,91344) (# 15463)
- supplementary design of 6-(27,12,29064) (# 15464) with respect to smaller t
- Tran van Trung construction (left) for 5-(26,12,54000) (# 15466) : der= 5-(26,11,25200) and res= 5-(26,12,54000) - the given design is the residual.
- residual design of 6-(28,12,34650) (# 15468)
- residual design of supplementary of 6-(28,12,39963) (# 15473)

- clan: 13-(32,16,450), 3 times reduced t, 3 times derived, 2 times residual
- residual design of 6-(28,13,79200) (# 11904)
- design 6-(27,13,54000) (# 15462) with respect to smaller t
- residual design of supplementary of 6-(28,13,91344) (# 15463)
- supplementary design of 6-(27,13,62280) (# 15465) with respect to smaller t
- Tran van Trung construction (right) for 5-(26,12,54000) (# 15466) : der= 5-(26,12,54000) and res= 5-(26,13,94500) - the given design is the derived.
- Tran van Trung construction (left) for 5-(26,13,94500) (# 15469) : der= 5-(26,12,54000) and res= 5-(26,13,94500) - the given design is the residual.
- derived from 6-(28,14,148500) (# 15470)
- derived from supplementary of 6-(28,14,171270) (# 15474)

- clan: 13-(32,16,519), 4 times reduced t, 3 times derived, 1 times residual
- supplementary design of 6-(28,13,79200) (# 11904) with respect to smaller t
- Tran van Trung construction (right) for 5-(27,12,91344) (# 11909) : der= 5-(27,12,91344) and res= 5-(27,13,171270) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,13,171270) (# 11910) : der= 5-(27,12,91344) and res= 5-(27,13,171270) - the given design is the residual.
- design 6-(28,13,91344) (# 15463) with respect to smaller t
- residual design of supplementary of 6-(29,13,113850) (# 15476)
- derived from supplementary of 6-(29,14,227700) (# 15479)
- residual design of 6-(29,13,131307) (# 15483)
- derived from 6-(29,14,262614) (# 15484)

- clan: 13-(32,16,519), 3 times reduced t, 4 times derived, 1 times residual
- derived from supplementary of 6-(28,13,79200) (# 11904)
- supplementary design of 6-(27,12,25200) (# 15461) with respect to smaller t
- derived from 6-(28,13,91344) (# 15463)
- design 6-(27,12,29064) (# 15464) with respect to smaller t
- Tran van Trung construction (left) for 5-(26,12,62280) (# 15467) : der= 5-(26,11,29064) and res= 5-(26,12,62280) - the given design is the residual.
- residual design of supplementary of 6-(28,12,34650) (# 15468)
- residual design of 6-(28,12,39963) (# 15473)

- clan: 13-(32,16,519), 3 times reduced t, 3 times derived, 2 times residual
- residual design of supplementary of 6-(28,13,79200) (# 11904)
- supplementary design of 6-(27,13,54000) (# 15462) with respect to smaller t
- residual design of 6-(28,13,91344) (# 15463)
- design 6-(27,13,62280) (# 15465) with respect to smaller t
- Tran van Trung construction (right) for 5-(26,12,62280) (# 15467) : der= 5-(26,12,62280) and res= 5-(26,13,108990) - the given design is the derived.
- derived from supplementary of 6-(28,14,148500) (# 15470)
- Tran van Trung construction (left) for 5-(26,13,108990) (# 15472) : der= 5-(26,12,62280) and res= 5-(26,13,108990) - the given design is the residual.
- derived from 6-(28,14,171270) (# 15474)

- clan: 13-(32,16,450), 4 times reduced t, 2 times derived, 2 times residual
- Tran van Trung construction with complementary design for 5-(27,13,148500) (# 11907)
- design 6-(28,14,148500) (# 15470) with respect to smaller t
- supplementary design of 6-(28,14,171270) (# 15474) with respect to smaller t
- Tran van Trung construction (left) for 5-(27,14,231000) (# 15477) : der= 5-(27,13,148500) and res= 5-(27,14,231000) - the given design is the residual.
- residual design of 6-(29,14,227700) (# 15479)
- residual design of supplementary of 6-(29,14,262614) (# 15484)
- derived from 6-(29,15,379500) (# 15496)
- derived from supplementary of 6-(29,15,437690) (# 15497)

- clan: 13-(32,16,519), 4 times reduced t, 2 times derived, 2 times residual
- Tran van Trung construction with complementary design for 5-(27,13,171270) (# 11910)
- supplementary design of 6-(28,14,148500) (# 15470) with respect to smaller t
- design 6-(28,14,171270) (# 15474) with respect to smaller t
- Tran van Trung construction (left) for 5-(27,14,266420) (# 15478) : der= 5-(27,13,171270) and res= 5-(27,14,266420) - the given design is the residual.
- residual design of supplementary of 6-(29,14,227700) (# 15479)
- residual design of 6-(29,14,262614) (# 15484)
- derived from supplementary of 6-(29,15,379500) (# 15496)
- derived from 6-(29,15,437690) (# 15497)

- clan: 13-(32,16,450), 5 times reduced t, 2 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(28,14,379500) (# 11911) : der= 5-(28,13,227700) and res= 5-(28,14,379500) - the given design is the residual.
- design 6-(29,14,227700) (# 15479) with respect to smaller t
- supplementary design of 6-(29,14,262614) (# 15484) with respect to smaller t
- residual design of 6-(30,14,341550) (# 15485)
- derived from 6-(30,15,607200) (# 15486)
- residual design of supplementary of 6-(30,14,393921) (# 15490)
- derived from supplementary of 6-(30,15,700304) (# 15491)

- clan: 13-(32,16,519), 5 times reduced t, 2 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(28,14,437690) (# 11912) : der= 5-(28,13,262614) and res= 5-(28,14,437690) - the given design is the residual.
- supplementary design of 6-(29,14,227700) (# 15479) with respect to smaller t
- design 6-(29,14,262614) (# 15484) with respect to smaller t
- residual design of supplementary of 6-(30,14,341550) (# 15485)
- derived from supplementary of 6-(30,15,607200) (# 15486)
- residual design of 6-(30,14,393921) (# 15490)
- derived from 6-(30,15,700304) (# 15491)

- clan: 13-(32,16,450), 6 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction with complementary design for 5-(29,14,607200) (# 11913)
- design 6-(30,15,607200) (# 15486) with respect to smaller t
- supplementary design of 6-(30,15,700304) (# 15491) with respect to smaller t
- residual design of 6-(31,15,948750) (# 15493)
- Tran van Trung construction (left) for 5-(29,15,910800) (# 15494) : der= 5-(29,14,607200) and res= 5-(29,15,910800) - the given design is the residual.
- residual design of supplementary of 6-(31,15,1094225) (# 15498)
- derived from 6-(31,16,1518000) (# 15507)
- derived from supplementary of 6-(31,16,1750760) (# 15508)

- clan: 13-(32,16,519), 6 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction with complementary design for 5-(29,14,700304) (# 11914)
- supplementary design of 6-(30,15,607200) (# 15486) with respect to smaller t
- design 6-(30,15,700304) (# 15491) with respect to smaller t
- residual design of supplementary of 6-(31,15,948750) (# 15493)
- Tran van Trung construction (left) for 5-(29,15,1050456) (# 15495) : der= 5-(29,14,700304) and res= 5-(29,15,1050456) - the given design is the residual.
- residual design of 6-(31,15,1094225) (# 15498)
- derived from supplementary of 6-(31,16,1518000) (# 15507)
- derived from 6-(31,16,1750760) (# 15508)

- clan: 13-(32,16,474), 3 times reduced t, 3 times derived, 1 times residual
- $Sp(6,2)$
- Tran van Trung construction (right) for 6-(27,12,26544) (# 13678) : der= 6-(27,12,26544) and res= 6-(27,13,56880) - the given design is the derived.
- Tran van Trung construction (left) for 6-(27,13,56880) (# 13679) : der= 6-(27,12,26544) and res= 6-(27,13,56880) - the given design is the residual.
- design 7-(28,13,26544) (# 15511) with respect to smaller t
- derived from 7-(29,14,83424) (# 15512)

- clan: 13-(32,16,495), 4 times reduced t, 3 times derived, 1 times residual
- supplementary design of 6-(28,13,83424) (# 11917) with respect to smaller t
- Tran van Trung construction (right) for 5-(27,12,87120) (# 11919) : der= 5-(27,12,87120) and res= 5-(27,13,163350) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,13,163350) (# 11920) : der= 5-(27,12,87120) and res= 5-(27,13,163350) - the given design is the residual.
- design 6-(28,13,87120) (# 11929) with respect to smaller t
- derived from supplementary of 6-(29,14,239844) (# 13690)
- derived from 6-(29,14,250470) (# 13693)

- clan: 13-(32,16,495), 3 times reduced t, 4 times derived, 1 times residual
- derived from supplementary of 6-(28,13,83424) (# 11917)
- derived from 6-(28,13,87120) (# 11929)
- Tran van Trung construction (left) for 5-(26,12,59400) (# 13676) : der= 5-(26,11,27720) and res= 5-(26,12,59400) - the given design is the residual.
- supplementary design of 6-(27,12,26544) (# 13678) with respect to smaller t
- design 6-(27,12,27720) (# 13680) with respect to smaller t

- clan: 13-(32,16,495), 3 times reduced t, 3 times derived, 2 times residual
- residual design of supplementary of 6-(28,13,83424) (# 11917)
- residual design of 6-(28,13,87120) (# 11929)
- Tran van Trung construction (right) for 5-(26,12,59400) (# 13676) : der= 5-(26,12,59400) and res= 5-(26,13,103950) - the given design is the derived.
- supplementary design of 6-(27,13,56880) (# 13679) with respect to smaller t
- design 6-(27,13,59400) (# 13681) with respect to smaller t
- derived from supplementary of 6-(28,14,156420) (# 13683)
- derived from 6-(28,14,163350) (# 13685)

- clan: 13-(32,16,495), 4 times reduced t, 2 times derived, 2 times residual
- Tran van Trung construction with complementary design for 5-(27,13,163350) (# 11920)
- supplementary design of 6-(28,14,156420) (# 13683) with respect to smaller t
- design 6-(28,14,163350) (# 13685) with respect to smaller t
- Tran van Trung construction (left) for 5-(27,14,254100) (# 13689) : der= 5-(27,13,163350) and res= 5-(27,14,254100) - the given design is the residual.
- residual design of supplementary of 6-(29,14,239844) (# 13690)
- residual design of 6-(29,14,250470) (# 13693)
- derived from supplementary of 6-(29,15,399740) (# 13704)
- derived from 6-(29,15,417450) (# 13705)

- clan: 13-(32,16,495), 5 times reduced t, 2 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(28,14,417450) (# 11921) : der= 5-(28,13,250470) and res= 5-(28,14,417450) - the given design is the residual.
- supplementary design of 6-(29,14,239844) (# 13690) with respect to smaller t
- design 6-(29,14,250470) (# 13693) with respect to smaller t
- derived from supplementary of 6-(30,15,639584) (# 13695)
- derived from 6-(30,15,667920) (# 13699)

- clan: 13-(32,16,495), 6 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction with complementary design for 5-(29,14,667920) (# 11922)
- supplementary design of 6-(30,15,639584) (# 13695) with respect to smaller t
- design 6-(30,15,667920) (# 13699) with respect to smaller t
- Tran van Trung construction (left) for 5-(29,15,1001880) (# 13703) : der= 5-(29,14,667920) and res= 5-(29,15,1001880) - the given design is the residual.

- clan: 14-(30,15,8), 6 times reduced t, 2 times derived
- Ajoodani-Namini Large Set recursion from 6-(14,7,4)

- clan: 14-(30,15,8), 7 times reduced t, 1 times derived
- Tran van Trung construction (right) for 6-(28,13,85272) (# 11924) : der= 6-(28,13,85272) and res= 6-(28,14,159885) - the given design is the derived.
- derived from 7-(30,15,245157) (# 11926)
- derived from supplementary of 7-(30,15,245157) (# 11926)

- clan: 14-(30,15,8), 7 times reduced t
- Alltop construction for design 6-(29,14,245157) (# 11925)
- Ajoodani-Namini Large Set recursion from 6-(14,7,4)

- clan: 14-(30,15,8), 7 times reduced t, 1 times residual
- residual design of 7-(30,15,245157) (# 11926)
- residual design of supplementary of 7-(30,15,245157) (# 11926)

- clan: 14-(30,15,8), 7 times reduced t, 2 times residual
- residual design of 6-(29,15,408595) (# 11927)
- residual design of supplementary of 6-(29,15,408595) (# 11927)

- clan: 13-(32,16,495), 3 times reduced t, 3 times derived, 1 times residual
- $Sp(6,2)$
- Tran van Trung construction (right) for 6-(27,12,27720) (# 13680) : der= 6-(27,12,27720) and res= 6-(27,13,59400) - the given design is the derived.
- Tran van Trung construction (left) for 6-(27,13,59400) (# 13681) : der= 6-(27,12,27720) and res= 6-(27,13,59400) - the given design is the residual.
- supplementary design of 7-(28,13,26544) (# 15511) with respect to smaller t
- derived from supplementary of 7-(29,14,83424) (# 15512)

- clan: 9-(31,10,6), 3 times derived
- $PSU(3,9)$ $\ge $ 22750 isomorphism types

- clan: 9-(31,10,6), 1 times reduced t, 3 times derived
- design 6-(28,7,6) (# 11930) with respect to smaller t
- Tran van Trung construction (right) for 5-(27,6,6) (# 11932) : der= 5-(27,6,6) and res= 5-(27,7,63) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,7,63) (# 11933) : der= 5-(27,6,6) and res= 5-(27,7,63) - the given design is the residual.
- derived from 6-(29,8,69) (# 11958)

- clan: 9-(31,10,6), 4 times derived
- derived from 6-(28,7,6) (# 11930)

- clan: 9-(31,10,6), 3 times derived, 1 times residual
- residual design of 6-(28,7,6) (# 11930)
- derived from 6-(28,8,63) (# 11954)

- clan: 9-(31,10,16), 1 times reduced t, 3 times derived
- supplementary design of 6-(28,7,6) (# 11930) with respect to smaller t
- Tran van Trung construction (right) for 5-(27,6,16) (# 11935) : der= 5-(27,6,16) and res= 5-(27,7,168) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,7,168) (# 11936) : der= 5-(27,6,16) and res= 5-(27,7,168) - the given design is the residual.
- derived from supplementary of 6-(29,8,69) (# 11958)

- clan: 9-(31,10,16), 4 times derived
- derived from supplementary of 6-(28,7,6) (# 11930)

- clan: 9-(31,10,16), 3 times derived, 1 times residual
- residual design of supplementary of 6-(28,7,6) (# 11930)
- derived from supplementary of 6-(28,8,63) (# 11954)

- clan: 9-(31,10,6), 2 times reduced t, 2 times derived
- Tran van Trung construction (right) for 5-(28,7,69) (# 11931) : der= 5-(28,7,69) and res= 5-(28,8,483) - the given design is the derived.
- design 6-(29,8,69) (# 11958) with respect to smaller t
- derived from 6-(30,9,552) (# 12115)

- clan: 9-(31,10,6), 3 times reduced t, 1 times derived
- Tran van Trung construction (right) for 5-(29,8,552) (# 11937) : der= 5-(29,8,552) and res= 5-(29,9,2898) - the given design is the derived.
- design 6-(30,9,552) (# 12115) with respect to smaller t
- derived from 6-(31,10,3450) (# 12218)

- clan: 9-(31,10,10), 2 times derived, 1 times residual
- $P\Gamma L(2,27)$ (38277 isom. types) \cite{Schmalz93}

- clan: 9-(31,10,10), 3 times derived, 1 times residual
- derived from 6-(28,8,105) (# 11939)

- clan: 9-(31,10,10), 2 times derived, 2 times residual
- residual design of 6-(28,8,105) (# 11939)

- clan: 9-(31,10,12), 3 times derived, 1 times residual
- derived from supplementary of 6-(28,8,105) (# 11939)

- clan: 9-(31,10,12), 2 times derived, 2 times residual
- residual design of supplementary of 6-(28,8,105) (# 11939)

- clan: 9-(31,10,4), 2 times derived, 1 times residual
- $P\Gamma L(2,27)$ (3 isom. types) \cite{Schmalz93}
- $P\Sigma L(2,27)$ (4308 isom. types)
- $P\GL(2,27)$ ($\ge 687$ isom. types)

- clan: 9-(31,10,4), 3 times derived, 1 times residual
- derived from 6-(28,8,42) (# 11944)

- clan: 9-(31,10,4), 2 times derived, 2 times residual
- residual design of 6-(28,8,42) (# 11944)
- derived from 6-(28,9,280) (# 11969)

- clan: 9-(31,10,18), 1 times reduced t, 2 times derived, 1 times residual
- supplementary design of 6-(28,8,42) (# 11944) with respect to smaller t
- Tran van Trung construction (right) for 5-(27,7,189) (# 11948) : der= 5-(27,7,189) and res= 5-(27,8,1260) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,8,1260) (# 11949) : der= 5-(27,7,189) and res= 5-(27,8,1260) - the given design is the residual.
- derived from supplementary of 6-(29,9,322) (# 11970)

- clan: 9-(31,10,18), 3 times derived, 1 times residual
- derived from supplementary of 6-(28,8,42) (# 11944)

- clan: 9-(31,10,18), 2 times derived, 2 times residual
- residual design of supplementary of 6-(28,8,42) (# 11944)
- derived from supplementary of 6-(28,9,280) (# 11969)

- clan: 9-(31,10,18), 1 times reduced t, 1 times derived, 2 times residual
- Tran van Trung construction (right) for 5-(27,8,1260) (# 11949) : der= 5-(27,8,1260) and res= 5-(27,9,5985) - the given design is the derived.
- supplementary design of 6-(28,9,280) (# 11969) with respect to smaller t
- residual design of supplementary of 6-(29,9,322) (# 11970)
- derived from supplementary of 6-(29,10,1610) (# 11971)

- clan: 9-(31,10,18), 2 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(28,9,7245) (# 11950) : der= 5-(28,8,1449) and res= 5-(28,9,7245) - the given design is the residual.
- supplementary design of 6-(29,9,322) (# 11970) with respect to smaller t
- derived from supplementary of 6-(30,10,1932) (# 11972)

- clan: 9-(31,10,18), 2 times reduced t, 2 times residual
- Tran van Trung construction (right) for 5-(28,9,7245) (# 11950) : der= 5-(28,9,7245) and res= 5-(28,10,27531) - the given design is the derived.
- supplementary design of 6-(29,10,1610) (# 11971) with respect to smaller t
- residual design of supplementary of 6-(30,10,1932) (# 11972)

- clan: 9-(31,10,18), 3 times reduced t, 1 times residual
- Tran van Trung construction (right) for 5-(29,9,8694) (# 11951) : der= 5-(29,9,8694) and res= 5-(29,10,34776) - the given design is the derived.
- Tran van Trung construction (left) for 5-(29,10,34776) (# 11952) : der= 5-(29,9,8694) and res= 5-(29,10,34776) - the given design is the residual.
- supplementary design of 6-(30,10,1932) (# 11972) with respect to smaller t

- clan: 9-(31,10,6), 2 times derived, 1 times residual
- $P\Gamma L(2,27)$ (367 isom. types) \cite{Schmalz93}
- $PSU(3,9)$ $\ge $ $\ge 107$ isomorphism types

- clan: 9-(31,10,6), 2 times derived, 2 times residual
- residual design of 6-(28,8,63) (# 11954)
- derived from 6-(28,9,420) (# 15828)
- derived from supplementary of 6-(28,9,1120) (# 15831)

- clan: 9-(31,10,16), 1 times reduced t, 2 times derived, 1 times residual
- supplementary design of 6-(28,8,63) (# 11954) with respect to smaller t
- Tran van Trung construction (left) for 5-(27,8,1120) (# 11957) : der= 5-(27,7,168) and res= 5-(27,8,1120) - the given design is the residual.
- residual design of supplementary of 6-(29,8,69) (# 11958)
- derived from supplementary of 6-(29,9,483) (# 12112)

- clan: 9-(31,10,16), 2 times derived, 2 times residual
- residual design of supplementary of 6-(28,8,63) (# 11954)
- derived from supplementary of 6-(28,9,420) (# 15828)
- derived from 6-(28,9,1120) (# 15831)

- clan: 9-(31,10,6), 1 times reduced t, 2 times derived
- Tran van Trung construction (left) for 6-(28,8,63) (# 11954) : der= 6-(28,7,6) and res= 6-(28,8,63) - the given design is the residual.

- clan: 9-(31,10,16), 2 times reduced t, 2 times derived
- Tran van Trung construction (left) for 5-(28,8,1288) (# 11956) : der= 5-(28,7,184) and res= 5-(28,8,1288) - the given design is the residual.
- supplementary design of 6-(29,8,69) (# 11958) with respect to smaller t
- derived from supplementary of 6-(30,9,552) (# 12115)

- clan: 9-(31,10,8), 2 times derived, 1 times residual
- $P\Gamma L(2,27)$ (21743 isom types) \cite{Schmalz93}

- clan: 9-(31,10,8), 3 times derived, 1 times residual
- derived from 6-(28,8,84) (# 11960)

- clan: 9-(31,10,8), 2 times derived, 2 times residual
- residual design of 6-(28,8,84) (# 11960)

- clan: 9-(31,10,14), 1 times reduced t, 2 times derived, 1 times residual
- supplementary design of 6-(28,8,84) (# 11960) with respect to smaller t
- Tran van Trung construction (right) for 5-(27,7,147) (# 11964) : der= 5-(27,7,147) and res= 5-(27,8,980) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,8,980) (# 11965) : der= 5-(27,7,147) and res= 5-(27,8,980) - the given design is the residual.

- clan: 9-(31,10,14), 3 times derived, 1 times residual
- derived from supplementary of 6-(28,8,84) (# 11960)

- clan: 9-(31,10,14), 2 times derived, 2 times residual
- residual design of supplementary of 6-(28,8,84) (# 11960)

- clan: 9-(31,10,8), 1 times reduced t, 1 times derived, 2 times residual
- Tran van Trung construction (right) for 5-(27,8,560) (# 11962) : der= 5-(27,8,560) and res= 5-(27,9,2660) - the given design is the derived.

- clan: 9-(31,10,8), 2 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(28,9,3220) (# 11966) : der= 5-(28,8,644) and res= 5-(28,9,3220) - the given design is the residual.

- clan: 9-(31,10,8), 3 times reduced t, 1 times derived
- Tran van Trung construction (left) for 5-(29,9,3864) (# 11967) : der= 5-(29,8,736) and res= 5-(29,9,3864) - the given design is the residual.

- clan: 9-(31,10,4), 1 times derived, 2 times residual
- $PSL(2,25)\oplus C_2\ \ge 201 solutions$

- clan: 9-(31,10,4), 1 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction (left) for 6-(28,9,280) (# 11969) : der= 6-(28,8,42) and res= 6-(28,9,280) - the given design is the residual.
- $P\Gamma L(2,27)+$ \cite{Bettenetal97b}

- clan: 9-(31,10,4), 1 times reduced t, 2 times residual
- Tran van Trung construction (right) for 6-(28,9,280) (# 11969) : der= 6-(28,9,280) and res= 6-(28,10,1330) - the given design is the derived.

- clan: 9-(31,10,4), 2 times reduced t, 1 times residual
- Tran van Trung construction (right) for 6-(29,9,322) (# 11970) : der= 6-(29,9,322) and res= 6-(29,10,1610) - the given design is the derived.
- Tran van Trung construction (left) for 6-(29,10,1610) (# 11971) : der= 6-(29,9,322) and res= 6-(29,10,1610) - the given design is the residual.

- clan: 8-(31,10,117), 2 times residual
- $P\Gamma L(2,27)+$ \cite{Bettenetal97b}
- residual design of 7-(30,10,819) (# 16029)

- clan: 8-(31,10,117), 1 times reduced t, 2 times residual
- design 6-(29,10,4095) (# 11973) with respect to smaller t
- Tran van Trung construction (left) for 5-(28,10,15561) (# 11975) : der= 5-(28,9,4095) and res= 5-(28,10,15561) - the given design is the residual.
- residual design of 6-(30,10,4914) (# 12170)
- residual design of supplementary of 6-(30,10,5712) (# 16030)
- supplementary design of 6-(29,10,4760) (# 16032) with respect to smaller t

- clan: 8-(31,10,117), 3 times residual
- residual design of 6-(29,10,4095) (# 11973)
- residual design of supplementary of 6-(29,10,4760) (# 16032)

- clan: 8-(31,10,136), 1 times reduced t, 2 times residual
- supplementary design of 6-(29,10,4095) (# 11973) with respect to smaller t
- Tran van Trung construction (right) for 5-(28,9,4760) (# 11977) : der= 5-(28,9,4760) and res= 5-(28,10,18088) - the given design is the derived.
- Tran van Trung construction (left) for 5-(28,10,18088) (# 11978) : der= 5-(28,9,4760) and res= 5-(28,10,18088) - the given design is the residual.
- residual design of supplementary of 6-(30,10,4914) (# 12170)
- residual design of 6-(30,10,5712) (# 16030)
- design 6-(29,10,4760) (# 16032) with respect to smaller t

- clan: 8-(31,10,136), 1 times derived, 2 times residual
- derived from supplementary of 6-(29,10,4095) (# 11973)
- residual design of supplementary of 6-(29,9,819) (# 12169)
- residual design of 6-(29,9,952) (# 16031)
- derived from 6-(29,10,4760) (# 16032)

- clan: 8-(31,10,136), 3 times residual
- residual design of supplementary of 6-(29,10,4095) (# 11973)
- residual design of 6-(29,10,4760) (# 16032)

- clan: 8-(31,10,117), 2 times reduced t, 1 times residual
- Tran van Trung construction (left) for 5-(29,10,19656) (# 11974) : der= 5-(29,9,4914) and res= 5-(29,10,19656) - the given design is the residual.
- design 6-(30,10,4914) (# 12170) with respect to smaller t
- supplementary design of 6-(30,10,5712) (# 16030) with respect to smaller t

- clan: 8-(31,10,136), 1 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(28,9,4760) (# 11977) : der= 5-(28,8,952) and res= 5-(28,9,4760) - the given design is the residual.
- supplementary design of 6-(29,9,819) (# 12169) with respect to smaller t
- derived from supplementary of 6-(30,10,4914) (# 12170)
- derived from 6-(30,10,5712) (# 16030)
- design 6-(29,9,952) (# 16031) with respect to smaller t

- clan: 8-(31,10,136), 2 times reduced t, 1 times residual
- Tran van Trung construction (right) for 5-(29,9,5712) (# 11980) : der= 5-(29,9,5712) and res= 5-(29,10,22848) - the given design is the derived.
- supplementary design of 6-(30,10,4914) (# 12170) with respect to smaller t
- design 6-(30,10,5712) (# 16030) with respect to smaller t

- clan: 8-(31,10,123), 2 times residual
- $P\Gamma L(2,27)+$ \cite{Bettenetal97b}
- residual design of 7-(30,10,861) (# 16042)

- clan: 8-(31,10,123), 1 times reduced t, 2 times residual
- design 6-(29,10,4305) (# 11982) with respect to smaller t
- Tran van Trung construction (left) for 5-(28,10,16359) (# 11984) : der= 5-(28,9,4305) and res= 5-(28,10,16359) - the given design is the residual.
- residual design of 6-(30,10,5166) (# 12180)
- residual design of supplementary of 6-(30,10,5460) (# 16043)
- supplementary design of 6-(29,10,4550) (# 16045) with respect to smaller t

- clan: 8-(31,10,123), 3 times residual
- residual design of 6-(29,10,4305) (# 11982)
- residual design of supplementary of 6-(29,10,4550) (# 16045)

- clan: 8-(31,10,130), 1 times reduced t, 2 times residual
- supplementary design of 6-(29,10,4305) (# 11982) with respect to smaller t
- Tran van Trung construction (right) for 5-(28,9,4550) (# 11986) : der= 5-(28,9,4550) and res= 5-(28,10,17290) - the given design is the derived.
- Tran van Trung construction (left) for 5-(28,10,17290) (# 11987) : der= 5-(28,9,4550) and res= 5-(28,10,17290) - the given design is the residual.
- residual design of supplementary of 6-(30,10,5166) (# 12180)
- residual design of 6-(30,10,5460) (# 16043)
- design 6-(29,10,4550) (# 16045) with respect to smaller t

- clan: 8-(31,10,130), 1 times derived, 2 times residual
- derived from supplementary of 6-(29,10,4305) (# 11982)
- residual design of supplementary of 6-(29,9,861) (# 12179)
- residual design of 6-(29,9,910) (# 16044)
- derived from 6-(29,10,4550) (# 16045)

- clan: 8-(31,10,130), 3 times residual
- residual design of supplementary of 6-(29,10,4305) (# 11982)
- residual design of 6-(29,10,4550) (# 16045)

- clan: 8-(31,10,123), 2 times reduced t, 1 times residual
- Tran van Trung construction (left) for 5-(29,10,20664) (# 11983) : der= 5-(29,9,5166) and res= 5-(29,10,20664) - the given design is the residual.
- design 6-(30,10,5166) (# 12180) with respect to smaller t
- supplementary design of 6-(30,10,5460) (# 16043) with respect to smaller t

- clan: 8-(31,10,130), 1 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(28,9,4550) (# 11986) : der= 5-(28,8,910) and res= 5-(28,9,4550) - the given design is the residual.
- supplementary design of 6-(29,9,861) (# 12179) with respect to smaller t
- derived from supplementary of 6-(30,10,5166) (# 12180)
- derived from 6-(30,10,5460) (# 16043)
- design 6-(29,9,910) (# 16044) with respect to smaller t

- clan: 8-(31,10,123), 3 times reduced t
- Tran van Trung construction (left) for 5-(30,10,25830) (# 11988) : der= 5-(30,9,6150) and res= 5-(30,10,25830) - the given design is the residual.

- clan: 8-(31,10,130), 2 times reduced t, 1 times residual
- Tran van Trung construction (right) for 5-(29,9,5460) (# 11989) : der= 5-(29,9,5460) and res= 5-(29,10,21840) - the given design is the derived.
- supplementary design of 6-(30,10,5166) (# 12180) with respect to smaller t
- design 6-(30,10,5460) (# 16043) with respect to smaller t

- clan: 21-(44,22,11), 15 times derived
- $PSU(3,9)+$ $\ge $ 30000 isomorphism types

- clan: 21-(44,22,11), 1 times reduced t, 15 times derived
- design 6-(29,7,11) (# 11992) with respect to smaller t
- Tran van Trung construction (left) for 5-(28,7,121) (# 11994) : der= 5-(28,6,11) and res= 5-(28,7,121) - the given design is the residual.

- clan: 21-(44,22,11), 15 times derived, 1 times residual
- residual design of 6-(29,7,11) (# 11992)

- clan: 21-(44,22,12), 1 times reduced t, 15 times derived
- supplementary design of 6-(29,7,11) (# 11992) with respect to smaller t
- Tran van Trung construction (left) for 5-(28,7,132) (# 11996) : der= 5-(28,6,12) and res= 5-(28,7,132) - the given design is the residual.

- clan: 21-(44,22,12), 15 times derived, 1 times residual
- residual design of supplementary of 6-(29,7,11) (# 11992)

- clan: 21-(44,22,11), 1 times reduced t, 14 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(28,7,121) (# 11994) : der= 5-(28,7,121) and res= 5-(28,8,847) - the given design is the derived.

- clan: 21-(44,22,12), 1 times reduced t, 14 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(28,7,132) (# 11996) : der= 5-(28,7,132) and res= 5-(28,8,924) - the given design is the derived.

- clan: 21-(44,22,11), 2 times reduced t, 14 times derived
- Tran van Trung construction (left) for 5-(29,8,968) (# 11997) : der= 5-(29,7,132) and res= 5-(29,8,968) - the given design is the residual.

created: Fri Oct 23 11:12:51 CEST 2009