t designs with small t, id ge 6000

# 6000: 5-(24,8,726)

clan: 13-(32,16,726), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6001: 5-(24,8,727)

clan: 5-(24,8,727)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6002: 5-(24,8,728)

clan: 5-(24,8,728)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6003: 5-(24,8,729)

clan: 13-(32,16,729), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,240) (# 10434)

# 6004: 5-(24,8,73)

clan: 5-(24,8,73)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6005: 5-(24,8,730)

clan: 5-(24,8,730)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6006: 5-(24,8,731)

clan: 6-(25,8,129), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6007: 5-(24,8,732)

clan: 13-(32,16,732), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6008: 5-(24,8,733)

clan: 5-(24,8,733)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6009: 5-(24,8,734)

clan: 5-(24,8,734)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6010: 5-(24,8,735)

clan: 13-(32,16,735), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6011: 5-(24,8,736)

clan: 5-(24,8,736)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6012: 5-(24,8,737)

clan: 5-(24,8,737)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6013: 5-(24,8,738)

clan: 13-(32,16,738), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6014: 5-(24,8,739)

clan: 5-(24,8,739)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6015: 5-(24,8,74)

clan: 5-(24,8,74)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6016: 5-(24,8,740)

clan: 5-(24,8,740)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6017: 5-(24,8,741)

clan: 15-(32,16,13), 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-(24,8,36) (# 9832) with respect to smaller t
Tran van Trung construction (right) for 5-(23,7,117) (# 9835) : der= 5-(23,7,117) and res= 5-(23,8,624) - the given design is the derived.
Tran van Trung construction (left) for 5-(23,8,624) (# 9836) : der= 5-(23,7,117) and res= 5-(23,8,624) - the given design is the residual.
design 6-(24,8,117) (# 13279) with respect to smaller t

# 6018: 5-(24,8,742)

clan: 5-(24,8,742)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6019: 5-(24,8,743)

clan: 5-(24,8,743)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6020: 5-(24,8,744)

clan: 13-(32,16,744), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,225) (# 10431)

# 6021: 5-(24,8,745)

clan: 5-(24,8,745)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6022: 5-(24,8,746)

clan: 5-(24,8,746)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6023: 5-(24,8,747)

clan: 13-(32,16,747), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6024: 5-(24,8,748)

clan: 6-(25,8,132), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6025: 5-(24,8,749)

clan: 5-(24,8,749)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6026: 5-(24,8,75)

clan: 13-(32,16,75), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6027: 5-(24,8,750)

clan: 13-(32,16,750), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6028: 5-(24,8,751)

clan: 5-(24,8,751)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6029: 5-(24,8,752)

clan: 5-(24,8,752)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6030: 5-(24,8,753)

clan: 13-(32,16,753), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6031: 5-(24,8,754)

clan: 5-(24,8,754)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6032: 5-(24,8,755)

clan: 5-(24,8,755)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6033: 5-(24,8,756)

clan: 13-(32,16,756), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6034: 5-(24,8,757)

clan: 5-(24,8,757)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6035: 5-(24,8,758)

clan: 5-(24,8,758)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6036: 5-(24,8,759)

clan: 13-(32,16,759), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6037: 5-(24,8,76)

clan: 6-(24,8,12), 1 times reduced t
$PGL(2,23)$

# 6038: 5-(24,8,760)

clan: 6-(24,8,120), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6039: 5-(24,8,761)

clan: 5-(24,8,761)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6040: 5-(24,8,762)

clan: 13-(32,16,762), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6041: 5-(24,8,763)

clan: 5-(24,8,763)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6042: 5-(24,8,764)

clan: 5-(24,8,764)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6043: 5-(24,8,765)

clan: 17-(36,18,15), 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-(25,8,36) (# 10396)
derived from supplementary of 6-(25,9,204) (# 10426)

# 6044: 5-(24,8,766)

clan: 5-(24,8,766)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6045: 5-(24,8,767)

clan: 5-(24,8,767)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6046: 5-(24,8,768)

clan: 13-(32,16,768), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6047: 5-(24,8,769)

clan: 5-(24,8,769)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6048: 5-(24,8,77)

clan: 5-(24,8,77)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6049: 5-(24,8,770)

clan: 5-(24,8,770)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6050: 5-(24,8,771)

clan: 13-(32,16,771), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6051: 5-(24,8,772)

clan: 5-(24,8,772)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6052: 5-(24,8,773)

clan: 5-(24,8,773)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6053: 5-(24,8,774)

clan: 13-(32,16,774), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6054: 5-(24,8,775)

clan: 5-(24,8,775)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6055: 5-(24,8,776)

clan: 5-(24,8,776)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6056: 5-(24,8,777)

clan: 13-(32,16,777), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6057: 5-(24,8,778)

clan: 5-(24,8,778)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6058: 5-(24,8,779)

clan: 6-(24,8,123), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6059: 5-(24,8,78)

clan: 13-(32,16,78), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6060: 5-(24,8,780)

clan: 13-(32,16,780), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,189) (# 10423)

# 6061: 5-(24,8,781)

clan: 5-(24,8,781)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6062: 5-(24,8,782)

clan: 6-(25,8,138), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6063: 5-(24,8,783)

clan: 13-(32,16,783), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6064: 5-(24,8,784)

clan: 5-(24,8,784)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6065: 5-(24,8,785)

clan: 5-(24,8,785)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6066: 5-(24,8,786)

clan: 13-(32,16,786), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6067: 5-(24,8,787)

clan: 5-(24,8,787)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6068: 5-(24,8,788)

clan: 5-(24,8,788)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6069: 5-(24,8,789)

clan: 13-(32,16,789), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,180) (# 10420)

# 6070: 5-(24,8,79)

clan: 5-(24,8,79)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6071: 5-(24,8,790)

clan: 5-(24,8,790)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6072: 5-(24,8,791)

clan: 5-(24,8,791)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6073: 5-(24,8,792)

clan: 13-(32,16,792), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6074: 5-(24,8,793)

clan: 5-(24,8,793)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6075: 5-(24,8,794)

clan: 5-(24,8,794)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6076: 5-(24,8,795)

clan: 13-(32,16,795), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6077: 5-(24,8,796)

clan: 5-(24,8,796)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6078: 5-(24,8,797)

clan: 5-(24,8,797)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6079: 5-(24,8,798)

clan: 15-(32,16,14), 2 times reduced t, 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6080: 5-(24,8,799)

clan: 6-(25,8,141), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6081: 5-(24,8,8)

clan: 5-(24,8,8)
\cite{KramerMagliveras74}

# 6082: 5-(24,8,80)

clan: 5-(24,8,80)
$PGL(2,23)$

# 6083: 5-(24,8,800)

clan: 5-(24,8,800)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6084: 5-(24,8,801)

clan: 13-(32,16,801), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6085: 5-(24,8,802)

clan: 5-(24,8,802)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6086: 5-(24,8,803)

clan: 5-(24,8,803)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6087: 5-(24,8,804)

clan: 13-(32,16,804), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6088: 5-(24,8,805)

clan: 5-(24,8,805)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6089: 5-(24,8,806)

clan: 5-(24,8,806)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6090: 5-(24,8,807)

clan: 13-(32,16,807), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6091: 5-(24,8,808)

clan: 5-(24,8,808)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6092: 5-(24,8,809)

clan: 5-(24,8,809)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6093: 5-(24,8,81)

clan: 13-(32,16,81), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6094: 5-(24,8,810)

clan: 13-(32,16,810), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6095: 5-(24,8,811)

clan: 5-(24,8,811)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6096: 5-(24,8,812)

clan: 5-(24,8,812)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6097: 5-(24,8,813)

clan: 13-(32,16,813), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6098: 5-(24,8,814)

clan: 5-(24,8,814)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 6099: 5-(24,8,815)

clan: 5-(24,8,815)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

created: Fri Oct 23 11:10:13 CEST 2009