´

t designs with small t, id ge 7600

# 7600: 5-(27,9,455)

clan: 6-(28,10,455), 1 times derived
$PGL(2,25)+$

# 7601: 5-(27,9,525)

clan: 6-(28,10,525), 1 times derived
$PGL(2,25)+$

# 7602: 5-(27,9,700)

clan: 6-(28,10,700), 1 times derived
$PGL(2,25)+$

# 7603: 5-(27,9,805)

clan: 6-(28,10,805), 1 times derived
$PGL(2,25)+$

# 7604: 5-(27,9,840)

# 7605: 5-(27,9,875)

clan: 6-(28,10,875), 1 times derived
$PGL(2,25)+$

# 7606: 5-(27,9,910)

# 7607: 5-(27,9,945)

# 7608: 5-(27,9,980)

clan: 6-(28,10,980), 1 times derived
$PGL(2,25)+$

# 7609: 5-(27,9,1050)

# 7610: 5-(27,9,1085)

clan: 6-(28,10,1085), 1 times derived
$PGL(2,25)+$

# 7611: 5-(27,9,1120)

# 7612: 5-(27,9,1190)

clan: 6-(28,10,1190), 1 times derived
$PGL(2,25)+$

# 7613: 5-(27,9,1225)

# 7614: 5-(27,9,1295)

clan: 6-(28,10,1295), 1 times derived
$PGL(2,25)+$

# 7615: 5-(27,9,1330)

clan: 9-(31,10,4), 1 times derived, 3 times residual
$PGL(2,25)+$
derived from 6-(28,10,1330) (# 11654)
residual design of 6-(28,9,280) (# 11969)

# 7616: 5-(27,9,1365)

# 7617: 5-(27,9,1400)

clan: 6-(28,10,1400), 1 times derived
$PGL(2,25)+$

# 7618: 5-(27,9,1435)

# 7619: 5-(27,9,1470)

# 7620: 5-(27,9,1505)

clan: 6-(28,10,1505), 1 times derived
$PGL(2,25)+$

# 7621: 5-(27,9,1575)

# 7622: 5-(27,9,1610)

clan: 6-(28,10,1610), 1 times derived
$PGL(2,25)+$

# 7623: 5-(27,9,1645)

clan: 6-(28,10,1645), 1 times derived
$PGL(2,25)+$
$ASL(3,3)^{13}$
derived from 6-(28,10,1645) (# 11686)

# 7624: 5-(27,9,1680)

# 7625: 5-(27,9,1715)

clan: 6-(28,10,1715), 1 times derived
$PGL(2,25)+$

# 7626: 5-(27,9,1750)

# 7627: 5-(27,9,1785)

clan: 6-(28,10,1785), 1 times derived
$PGL(2,25)+$

# 7628: 5-(27,9,1820)

clan: 6-(28,10,1820), 1 times derived
$PGL(2,25)+$

# 7629: 5-(27,9,1855)

clan: 6-(28,10,1855), 1 times derived
$PGL(2,25)+$

# 7630: 5-(27,9,1890)

# 7631: 5-(27,9,1960)

clan: 6-(28,10,1960), 1 times derived
$PGL(2,25)+$

# 7632: 5-(27,9,1995)

clan: 9-(31,10,6), 1 times derived, 3 times residual
$PGL(2,25)+$
residual design of 6-(28,9,420) (# 15828)
derived from 6-(28,10,1995) (# 15829)
residual design of supplementary of 6-(28,9,1120) (# 15831)
derived from supplementary of 6-(28,10,5320) (# 15832)

# 7633: 5-(27,9,2030)

clan: 6-(28,10,2030), 1 times derived
$PGL(2,25)+$

# 7634: 5-(27,9,2065)

clan: 6-(28,10,2065), 1 times derived
$PGL(2,25)+$

# 7635: 5-(27,9,2100)

clan: 6-(28,10,2100), 1 times derived
$PGL(2,25)+$

# 7636: 5-(27,9,2135)

clan: 6-(28,10,2135), 1 times derived
$PGL(2,25)+$

# 7637: 5-(27,9,2170)

# 7638: 5-(27,9,2205)

clan: 6-(28,10,2205), 1 times derived
$PGL(2,25)+$
$PGL(2,25)+$
derived from 6-(28,10,2205) (# 11714)

# 7639: 5-(27,9,2240)

clan: 6-(28,10,2240), 1 times derived
$PGL(2,25)+$

# 7640: 5-(27,9,2275)

clan: 6-(28,10,2275), 1 times derived
$PGL(2,25)+$

# 7641: 5-(27,9,2345)

clan: 6-(28,10,2345), 1 times derived
$PGL(2,25)+$

# 7642: 5-(27,9,2380)

clan: 6-(28,10,2380), 1 times derived
$PGL(2,25)+$

# 7643: 5-(27,9,2415)

clan: 6-(28,10,2415), 1 times derived
$PGL(2,25)+$

# 7644: 5-(27,9,2450)

clan: 6-(28,10,2450), 1 times derived
$PGL(2,25)+$

# 7645: 5-(27,9,2485)

clan: 6-(28,10,2485), 1 times derived
$PGL(2,25)+$

# 7646: 5-(27,9,2520)

# 7647: 5-(27,9,2555)

clan: 6-(28,10,2555), 1 times derived
$PGL(2,25)+$

# 7648: 5-(27,9,2590)

# 7649: 5-(27,9,2625)

clan: 6-(28,10,2625), 1 times derived
$PGL(2,25)+$

# 7650: 5-(27,9,2660)

clan: 9-(31,10,8), 1 times derived, 3 times residual
$PGL(2,25)+$

# 7651: 5-(27,9,2730)

clan: 6-(28,10,2730), 1 times derived
$PGL(2,25)+$

# 7652: 5-(27,9,2765)

clan: 6-(28,10,2765), 1 times derived
$PGL(2,25)+$

# 7653: 5-(27,9,2800)

# 7654: 5-(27,9,2835)

clan: 6-(28,10,2835), 1 times derived
$PGL(2,25)+$

# 7655: 5-(27,9,2870)

clan: 6-(28,10,2870), 1 times derived
$PGL(2,25)+$

# 7656: 5-(27,9,2905)

# 7657: 5-(27,9,2940)

# 7658: 5-(27,9,2975)

clan: 6-(28,10,2975), 1 times derived
$PGL(2,25)+$

# 7659: 5-(27,9,3010)

clan: 6-(28,10,3010), 1 times derived
$PGL(2,25)+$

# 7660: 5-(27,9,3045)

clan: 6-(28,10,3045), 1 times derived
$PGL(2,25)+$

# 7661: 5-(27,9,3115)

# 7662: 5-(27,9,3150)

# 7663: 5-(27,9,3185)

clan: 6-(28,10,3185), 1 times derived
$PGL(2,25)+$

# 7664: 5-(27,9,3220)

clan: 6-(28,10,3220), 1 times derived
$PGL(2,25)+$
derived from 6-(28,10,3220) (# 11762)
derived from supplementary of 6-(28,10,4095) (# 11800)

# 7665: 5-(27,9,3255)

# 7666: 5-(27,9,3290)

clan: 6-(28,10,3290), 1 times derived
$PGL(2,25)+$

# 7667: 5-(27,9,3325)

clan: 9-(31,10,10), 1 times derived, 3 times residual
$PGL(2,25)+$

# 7668: 5-(27,9,3360)

clan: 6-(28,10,3360), 1 times derived
$PGL(2,25)+$

# 7669: 5-(27,9,3395)

clan: 6-(28,10,3395), 1 times derived
$PGL(2,25)+$

# 7670: 5-(27,9,3430)

clan: 6-(28,10,3430), 1 times derived
$PGL(2,25)+$
derived from 6-(28,10,3430) (# 11774)
derived from supplementary of 6-(28,10,3885) (# 11799)

# 7671: 5-(27,9,3500)

clan: 6-(28,10,3500), 1 times derived
$PGL(2,25)+$

# 7672: 5-(27,9,3535)

clan: 6-(28,10,3535), 1 times derived
$PGL(2,25)+$
derived from 6-(28,10,3535) (# 11780)
derived from supplementary of 6-(28,10,3780) (# 11798)

# 7673: 5-(27,9,3570)

clan: 6-(28,10,3570), 1 times derived
$PGL(2,25)+$
derived from 6-(28,10,3570) (# 11786)
derived from supplementary of 6-(28,10,3745) (# 11797)

# 7674: 5-(27,9,3605)

clan: 6-(28,10,3605), 1 times derived
$PGL(2,25)+$

# 7675: 5-(27,9,3640)

clan: 6-(28,10,3640), 1 times derived
$PGL(2,25)+$
derived from 6-(28,10,3640) (# 11791)
derived from supplementary of 6-(28,10,3675) (# 11796)

# 7676: 5-(27,9,3675)

clan: 6-(28,10,3675), 1 times derived
$PGL(2,25)+$
derived from supplementary of 6-(28,10,3640) (# 11791)
derived from 6-(28,10,3675) (# 11796)

# 7677: 5-(27,9,3710)

clan: 6-(28,10,3710), 1 times derived
$PGL(2,25)+$

# 7678: 5-(27,9,3745)

clan: 6-(28,10,3745), 1 times derived
$PGL(2,25)+$
derived from supplementary of 6-(28,10,3570) (# 11786)
derived from 6-(28,10,3745) (# 11797)

# 7679: 5-(27,10,2394)

clan: 9-(31,10,2), 4 times residual
$PGL(2,25)+$

# 7680: 5-(27,10,4284)

clan: 6-(28,10,1190), 1 times residual
$PGL(2,25)+$

# 7681: 5-(28,10,5474)

clan: 6-(28,10,1190), 1 times reduced t
Tran van Trung construction (left) for 5-(27,10,4284) (# 7680) : der= 5-(27,9,1190) and res= 5-(27,10,4284) - the given design is the residual.

# 7682: 5-(27,10,6174)

clan: 6-(28,10,1715), 1 times residual
$PGL(2,25)+$

# 7683: 5-(28,10,7889)

clan: 6-(28,10,1715), 1 times reduced t
Tran van Trung construction (left) for 5-(27,10,6174) (# 7682) : der= 5-(27,9,1715) and res= 5-(27,10,6174) - the given design is the residual.

# 7684: 5-(27,10,6300)

clan: 6-(28,10,1750), 1 times residual
$PGL(2,25)+$
residual design of 6-(28,10,1750) (# 11698)

# 7685: 5-(28,10,8050)

clan: 6-(28,10,1750), 1 times reduced t
Tran van Trung construction (left) for 5-(27,10,6300) (# 7684) : der= 5-(27,9,1750) and res= 5-(27,10,6300) - the given design is the residual.
design 6-(28,10,1750) (# 11698) with respect to smaller t

# 7686: 5-(27,10,7560)

clan: 6-(28,10,2100), 1 times residual
$PGL(2,25)+$

# 7687: 5-(28,10,9660)

clan: 6-(28,10,2100), 1 times reduced t
Tran van Trung construction (left) for 5-(27,10,7560) (# 7686) : der= 5-(27,9,2100) and res= 5-(27,10,7560) - the given design is the residual.

# 7688: 5-(28,10,10080)

clan: 5-(28,10,10080)
\cite{Sebille98} $Sp(6,2)$ <= 5359 isomorphism types

# 7689: 5-(28,10,11760)

clan: 5-(28,10,11760)
\cite{Sebille98} $Sp(6,2)$ <= 7037 isomorphism types

# 7690: 5-(28,10,12600)

clan: 5-(28,10,12600)
\cite{Sebille98} $Sp(6,2)$ <= 15643 isomorphism types

# 7691: 5-(28,10,13069)

clan: 5-(28,10,13069)
\cite{Sebille98} $Sp(6,2)$ <= 17036 isomorphism types

# 7692: 5-(28,10,2149)

clan: 5-(28,10,2149)
\cite{Sebille98} $Sp(6,2)$ 1 isomorphism type

# 7693: 5-(28,10,2940)

clan: 5-(28,10,2940)
\cite{Sebille98} $Sp(6,2)$ 1-3 isomorphism types

# 7694: 5-(28,10,2989)

clan: 5-(28,10,2989)
\cite{Sebille98} $Sp(6,2)$ 1 isomorphism type

# 7695: 5-(28,10,5040)

clan: 5-(28,10,5040)
\cite{Sebille98} $Sp(6,2)$ 129 isomorphism types

# 7696: 5-(28,10,6720)

clan: 5-(28,10,6720)
\cite{Sebille98} $Sp(6,2)$ 412 isomorphism types

# 7697: 5-(28,10,7560)

clan: 5-(28,10,7560)
\cite{Sebille98} $Sp(6,2)$ 810 isomorphism types

# 7698: 5-(28,12,108537)

clan: 13-(32,16,429), 4 times reduced t, 4 times derived
\cite{Sebille98} $Sp(6,2)$
Tran van Trung construction (right) for 5-(27,11,33033) (# 10200) : der= 5-(27,11,33033) and res= 5-(27,12,75504) - the given design is the derived.
Tran van Trung construction (left) for 5-(27,12,75504) (# 10201) : der= 5-(27,11,33033) and res= 5-(27,12,75504) - the given design is the residual.
design 6-(28,12,33033) (# 13633) with respect to smaller t
derived from 6-(29,13,108537) (# 13636)
supplementary design of 6-(28,12,41580) (# 14258) with respect to smaller t
derived from supplementary of 6-(29,13,136620) (# 14259)

# 7699: 5-(28,12,136620)

clan: 13-(32,16,540), 4 times reduced t, 4 times derived
\cite{Sebille98} $Sp(6,2)$
Tran van Trung construction (left) for 5-(27,12,95040) (# 11393) : der= 5-(27,11,41580) and res= 5-(27,12,95040) - the given design is the residual.
supplementary design of 6-(28,12,33033) (# 13633) with respect to smaller t
derived from supplementary of 6-(29,13,108537) (# 13636)
design 6-(28,12,41580) (# 14258) with respect to smaller t
derived from 6-(29,13,136620) (# 14259)

created: Fri Oct 23 11:11:30 CEST 2009

University of Bayreuth -