t designs with small t, id ge 0

---

# 0: 3-(12,6,4)

• clan: 3-(12,6,4)
• $Aut(Icosahedron)$ 1 solution

---

# 1: 3-(14,5,5)

• clan: 9-(20,10,1), 5 times derived, 1 times residual
• $D_7\times C_2$ 42 solutions

---

# 2: 3-(16,4,1)

• clan: 11-(24,12,1), 8 times derived
• $Aut(4-Cube)$

---

# 3: 3-(16,5,12)

• clan: 11-(24,12,2), 7 times derived, 1 times residual
• $Aut(4-Cube)$

---

# 4: 3-(16,8,3)

• clan: 3-(16,8,3)
• $Aut(4-Cube)$

---

# 5: 3-(16,8,12)

• clan: 3-(16,8,12)
• $Aut(4-Cube)$

---

# 6: 3-(20,4,1)

• clan: 15-(32,16,1), 12 times derived
• $Aut(Dodecahedron)$

---

# 7: 3-(20,5,8)

• clan: 15-(32,16,1), 11 times derived, 1 times residual
• $D_{19}+$

---

# 8: 3-(20,9,728)

• clan: 15-(32,16,1), 7 times derived, 5 times residual
• $PSL(3,4)-$

---

# 9: 3-(22,5,3)

• clan: 6-(25,8,3), 3 times derived
• $PSL(2,11)$ 1 solution

---

# 10: 3-(22,6,1)

• clan: 5-(24,8,1), 2 times derived
• $PSL(2,11)$ 1 solution

---

# 11: 3-(22,7,8)

• clan: 5-(24,8,2), 1 times derived, 1 times residual
• $PSL(2,11)$ 1 solution

---

# 12: 3-(22,8,12)

• clan: 5-(24,8,1), 2 times residual
• $PSL(2,11)$ 1 solution

---

# 13: 3-(22,9,84)

• clan: 13-(32,16,3), 7 times derived, 3 times residual
• $PSL(2,11)$ 35 solutions

---

# 14: 3-(22,9,126)

• clan: 11-(30,15,18), 6 times derived, 2 times residual
• $PSL(2,11)$ 2804 solutions

---

# 15: 3-(32,16,7)

• clan: 3-(32,16,7)
• $AGL(5,2)$ 1 isomorphism type

---

# 16: 3-(64,4,1)

• clan: 59-(120,60,1), 56 times derived
• $SL(3,4)$ 1 isomorphism type

---

# 17: 4-(11,5,1)

• clan: 5-(12,6,1), 1 times derived
• \cite{Witt38}

---

# 18: 5-(12,6,1)

• clan: 5-(12,6,1)
• Alltop construction for design 4-(11,5,1) (# 17)
• \cite{Witt38} $M_{12}$ (1 isom. type)

---

# 19: 4-(11,5,2)

• clan: 5-(12,6,2), 1 times derived
• \cite{Kramer74}

---

# 20: 5-(12,6,2)

• clan: 5-(12,6,2)
• Alltop construction for design 4-(11,5,2) (# 19)
• $Aut(Icosahedron)$, $PGL(2,11)$ supplementary design has same parameters

---

# 21: 4-(11,5,3)

• clan: 5-(12,6,3), 1 times derived
• \cite{Brouwer86}

---

# 22: 5-(12,6,3)

• clan: 5-(12,6,3)
• Alltop construction for design 4-(11,5,3) (# 21)
• $(C_2\times C_2)\times C_3$, 36 solutions
• $(A_3)\times C_3$, 24 solutions
• $(A_4)_6\times C_2$, 8 solutions

---

# 23: 4-(15,5,2)

• clan: 9-(20,10,2), 5 times derived
• $C_{14}+$ 18 isomorphism types

---

# 24: 4-(15,7,20)

• clan: 5-(16,8,20), 1 times derived
• $Hol(C_5)C_3$ Wassermann

---

# 25: 5-(16,8,20)

• clan: 5-(16,8,20)
• Alltop construction for design 4-(15,7,20) (# 24)

---

# 26: 4-(15,7,25)

• clan: 5-(16,8,25), 1 times derived
• $Hol(C_5)C_3$ Wassermann

---

# 27: 5-(16,8,25)

• clan: 5-(16,8,25)
• Alltop construction for design 4-(15,7,25) (# 26)

---

# 28: 4-(15,7,30)

• clan: 9-(20,10,2), 3 times derived, 2 times residual
• Brouwer 1977/1986

---

# 29: 5-(16,8,30)

• clan: 9-(20,10,2), 2 times derived, 2 times residual
• Alltop construction for design 4-(15,7,30) (# 28)

---

# 30: 4-(15,7,35)

• clan: 5-(16,8,35), 1 times derived
• Brouwer 1977/1986

---

# 31: 5-(16,8,35)

• clan: 5-(16,8,35)
• Alltop construction for design 4-(15,7,35) (# 30)

---

# 32: 4-(15,7,40)

• clan: 5-(16,8,40), 1 times derived
• Brouwer 1977/1986

---

# 33: 5-(16,8,40)

• clan: 5-(16,8,40)
• Alltop construction for design 4-(15,7,40) (# 32)

---

# 34: 4-(15,7,45)

• clan: 9-(20,10,3), 3 times derived, 2 times residual
• Brouwer 1977/1986

---

# 35: 5-(16,8,45)

• clan: 9-(20,10,3), 2 times derived, 2 times residual
• Alltop construction for design 4-(15,7,45) (# 34)
• $A_4\times D_4$ 1322 solutions

---

# 36: 4-(15,7,50)

• clan: 5-(16,8,50), 1 times derived
• Brouwer 1977/1986

---

# 37: 5-(16,8,50)

• clan: 5-(16,8,50)
• Alltop construction for design 4-(15,7,50) (# 36)

---

# 38: 4-(15,7,55)

• clan: 7-(16,8,3), 2 times reduced t, 1 times derived
• Brouwer 1977/1986

---

# 39: 5-(16,8,55)

• clan: 7-(16,8,3), 2 times reduced t
• Alltop construction for design 4-(15,7,55) (# 38)
• Tran van Trung construction with complementary design for 5-(15,7,15) (# 422)
• Tran van Trung construction (right) for 5-(15,7,15) (# 422) : der= 5-(15,7,15) and res= 5-(15,8,40) - the given design is the derived.
• Tran van Trung construction (left) for 5-(15,8,40) (# 423) : der= 5-(15,7,15) and res= 5-(15,8,40) - the given design is the residual.

---

# 40: 4-(15,7,60)

• clan: 9-(20,10,4), 3 times derived, 2 times residual
• Brouwer 1977/1986

---

# 41: 5-(16,8,60)

• clan: 9-(20,10,4), 2 times derived, 2 times residual
• Alltop construction for design 4-(15,7,60) (# 40)
• $A_4\times A_4$

---

# 42: 4-(15,7,65)

• clan: 5-(16,8,65), 1 times derived
• Brouwer 1977/1986

---

# 43: 5-(16,8,65)

• clan: 5-(16,8,65)
• Alltop construction for design 4-(15,7,65) (# 42)
• $A_4\times A_4$

---

# 44: 4-(15,7,70)

• clan: 5-(16,8,70), 1 times derived
• Brouwer 1977/1986

---

# 45: 5-(16,8,70)

• clan: 5-(16,8,70)
• Alltop construction for design 4-(15,7,70) (# 44)

---

# 46: 4-(15,7,75)

• clan: 9-(20,10,5), 3 times derived, 2 times residual
• Brouwer 1977/1986

---

# 47: 5-(16,8,75)

• clan: 9-(20,10,5), 2 times derived, 2 times residual
• Alltop construction for design 4-(15,7,75) (# 46)

---

# 48: 4-(15,7,80)

• clan: 5-(16,8,80), 1 times derived
• Brouwer 1977/1986

---

# 49: 5-(16,8,80)

• clan: 5-(16,8,80)
• Alltop construction for design 4-(15,7,80) (# 48)

---

# 50: 4-(16,6,6)

• clan: 9-(20,10,1), 1 times reduced t, 4 times derived
• $(D_5\times C_3)+$ Wassermann

---

# 51: 4-(17,5,3)

• clan: 11-(24,12,3), 7 times derived
• $C_{17}$ Laue05

---

# 52: 4-(17,5,6)

• clan: 11-(24,12,6), 7 times derived
• $D_{17})$ Wassermann

---

# 53: 4-(17,8,290)

• clan: 7-(20,10,116), 2 times derived, 1 times residual
• $C_{17}C8$ Wassermann

---

# 54: 5-(18,9,290)

• clan: 7-(20,10,116), 1 times derived, 1 times residual
• Alltop construction for design 4-(17,8,290) (# 53)
• residual design of 6-(19,9,116) (# 8618)
• derived from 6-(19,10,290) (# 8622)
• residual design of supplementary of 6-(19,9,170) (# 8626)
• derived from supplementary of 6-(19,10,425) (# 8627)

---

# 55: 4-(18,6,34)

• clan: 4-(18,6,34)
• $Hol(C_{17})+$

---

# 56: 4-(18,6,38)

• clan: 4-(18,6,38)
• $Hol(C_{17})+$

---

# 57: 4-(18,6,41)

• clan: 4-(18,6,41)
• $Hol(C_{17})+$

---

# 58: 4-(18,6,44)

• clan: 4-(18,6,44)
• $Hol(C_{17})+$

---

# 59: 4-(18,6,45)

• clan: 4-(18,6,45)
• $T(2,3) \wr C_2$

---

# 60: 4-(21,6,48)

• clan: 15-(32,16,6), 10 times derived, 1 times residual
• $Aut(Dodecahedron)+$
• $A_7^{[2]}$ 8 solutions, $Hol(C_{21})$ many solutions

---

# 61: 4-(21,10,1036)

• clan: 7-(24,12,518), 2 times derived, 1 times residual
• ${\bf PSL(2,19)}^+ $% -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 62: 5-(22,11,1036)

• clan: 7-(24,12,518), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1036) (# 61)

---

# 63: 4-(21,10,1092)

• clan: 13-(30,15,12), 5 times derived, 4 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 64: 5-(22,11,1092)

• clan: 13-(30,15,12), 4 times derived, 4 times residual
• Alltop construction for design 4-(21,10,1092) (# 63)

---

# 65: 4-(21,10,1120)

• clan: 7-(24,12,560), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $% -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 66: 5-(22,11,1120)

• clan: 7-(24,12,560), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1120) (# 65)
• \cite{Kreher95} $PSL(3,4)+$ 9 isomorphism types $PGL(2,19)++$

---

# 67: 4-(21,10,1176)

• clan: 7-(24,12,588), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 68: 5-(22,11,1176)

• clan: 7-(24,12,588), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1176) (# 67)

---

# 69: 4-(21,10,1204)

• clan: 7-(24,12,602), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 70: 5-(22,11,1204)

• clan: 7-(24,12,602), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1204) (# 69)

---

# 71: 4-(21,10,1260)

• clan: 7-(24,12,630), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $% -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 72: 5-(22,11,1260)

• clan: 7-(24,12,630), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1260) (# 71)

---

# 73: 4-(21,10,1344)

• clan: 7-(24,12,672), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 74: 5-(22,11,1344)

• clan: 7-(24,12,672), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1344) (# 73)
• $PSL(3,4)+$ 9 isomorphism types

---

# 75: 4-(21,10,1372)

• clan: 7-(24,12,686), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $% -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 76: 5-(22,11,1372)

• clan: 7-(24,12,686), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1372) (# 75)

---

# 77: 4-(21,10,1456)

• clan: 15-(32,16,2), 6 times derived, 5 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+
• PSL(3,4)

---

# 78: 5-(22,11,1456)

• clan: 15-(32,16,2), 5 times derived, 5 times residual
• Alltop construction for design 4-(21,10,1456) (# 77)
• \cite{Kreher95} $PSL(3,4)+$ $PGL(2,19)++$

---

# 79: 4-(21,10,1512)

• clan: 7-(24,12,756), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $% -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 80: 5-(22,11,1512)

• clan: 7-(24,12,756), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1512) (# 79)
• \cite{Kreher95} $PSL(3,4)+$

---

# 81: 4-(21,10,1540)

• clan: 7-(24,12,770), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 82: 5-(22,11,1540)

• clan: 7-(24,12,770), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1540) (# 81)
• residual design of 6-(23,11,770) (# 9721)
• derived from 6-(23,12,1540) (# 9724)
• residual design of supplementary of 6-(23,11,5418) (# 9732)
• derived from supplementary of 6-(23,12,10836) (# 9733)

---

# 83: 4-(21,10,1596)

• clan: 7-(24,12,798), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 84: 5-(22,11,1596)

• clan: 7-(24,12,798), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1596) (# 83)

---

# 85: 4-(21,10,1624)

• clan: 7-(24,12,812), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 86: 5-(22,11,1624)

• clan: 7-(24,12,812), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1624) (# 85)

---

# 87: 4-(21,10,1680)

• clan: 7-(24,12,840), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+
• PGL(3,4)

---

# 88: 5-(22,11,1680)

• clan: 7-(24,12,840), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1680) (# 87)
• PGL(3,4)+ Alltop construction from 4-(21,10,1680)
• \cite{Kreher95} $PSL(3,4)+$ $PGL(2,19)++$

---

# 89: 4-(21,10,1764)

• clan: 7-(24,12,882), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 90: 5-(22,11,1764)

• clan: 7-(24,12,882), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1764) (# 89)
• $PGL(2,19)++$
• residual design of 6-(23,11,882) (# 9737)
• derived from 6-(23,12,1764) (# 9740)
• residual design of supplementary of 6-(23,11,5306) (# 9748)
• derived from supplementary of 6-(23,12,10612) (# 9749)

---

# 91: 4-(21,10,1792)

• clan: 7-(24,12,896), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $% -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 92: 5-(22,11,1792)

• clan: 7-(24,12,896), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1792) (# 91)
• \cite{Kreher95}
• residual design of 6-(23,11,896) (# 9753)
• derived from 6-(23,12,1792) (# 9756)
• residual design of supplementary of 6-(23,11,5292) (# 9764)
• derived from supplementary of 6-(23,12,10584) (# 9765)

---

# 93: 4-(21,10,1876)

• clan: 7-(24,12,938), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 94: 5-(22,11,1876)

• clan: 7-(24,12,938), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1876) (# 93)
• residual design of 6-(23,11,938) (# 9769)
• derived from 6-(23,12,1876) (# 9772)
• residual design of supplementary of 6-(23,11,5250) (# 9780)
• derived from supplementary of 6-(23,12,10500) (# 9781)

---

# 95: 4-(21,10,1932)

• clan: 7-(24,12,966), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 96: 5-(22,11,1932)

• clan: 7-(24,12,966), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1932) (# 95)

---

# 97: 4-(21,10,1960)

• clan: 7-(24,12,980), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 98: 5-(22,11,1960)

• clan: 7-(24,12,980), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,1960) (# 97)
• \cite{Kreher95}

---

# 99: 4-(21,10,2016)

• clan: 7-(24,12,1008), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

---

created: Fri Oct 23 11:09:27 CEST 2009