t designs with small t, id ge 7700

---

# 7700: 5-(28,14,213785)

• clan: 11-(30,15,1014), 4 times reduced t, 1 times derived, 1 times residual
• \cite{Sebille98} $AGL(3,3)+$
• Tran van Trung construction with complementary design for 5-(27,13,83655) (# 11093)
• design 6-(28,14,83655) (# 11096) with respect to smaller t
• Tran van Trung construction (left) for 5-(27,14,130130) (# 11101) : der= 5-(27,13,83655) and res= 5-(27,14,130130) - the given design is the residual.
• supplementary design of 6-(28,14,236115) (# 11105) with respect to smaller t

---

# 7701: 5-(28,14,77220)

• clan: 9-(32,16,23166), 2 times derived, 2 times residual
• $PGL(2,25)++$

---

# 7702: 5-(28,14,169400)

• clan: 9-(32,16,50820), 2 times derived, 2 times residual
• $PGL(2,25)++$

---

# 7703: 5-(28,14,232375)

• clan: 7-(30,15,139425), 1 times derived, 1 times residual
• $PGL(2,25)++$

---

# 7704: 5-(28,14,95095)

• clan: 7-(30,15,57057), 1 times derived, 1 times residual
• $PGL(2,25)++$

---

# 7705: 5-(28,14,35035)

• clan: 7-(30,15,21021), 1 times derived, 1 times residual
• $PGL(2,25)++$

---

# 7706: 5-(28,14,312455)

• clan: 13-(30,15,52), 6 times reduced t, 1 times derived, 1 times residual
• \cite{Sebille98} $AGL(3,3)+$
• Tran van Trung construction with complementary design for 5-(27,13,122265) (# 11285)
• design 6-(28,14,122265) (# 11288) with respect to smaller t
• Tran van Trung construction (left) for 5-(27,14,190190) (# 11293) : der= 5-(27,13,122265) and res= 5-(27,14,190190) - the given design is the residual.
• supplementary design of 6-(28,14,197505) (# 11297) with respect to smaller t

---

# 7707: 5-(28,14,361790)

• clan: 13-(32,16,429), 4 times reduced t, 2 times derived, 2 times residual
• \cite{Sebille98} $AGL(3,3)+$
• Tran van Trung construction with complementary design for 5-(27,13,141570) (# 10202)
• design 6-(28,14,141570) (# 11382) with respect to smaller t
• Tran van Trung construction (left) for 5-(27,14,220220) (# 11386) : der= 5-(27,13,141570) and res= 5-(27,14,220220) - the given design is the residual.
• supplementary design of 6-(28,14,178200) (# 11390) with respect to smaller t
• residual design of 6-(29,14,217074) (# 13637)
• residual design of supplementary of 6-(29,14,273240) (# 13638)
• derived from 6-(29,15,361790) (# 13647)
• derived from supplementary of 6-(29,15,455400) (# 13648)

---

# 7708: 5-(28,6,10)

• clan: 21-(44,22,10), 16 times derived
• $PSL(2,27)$ 22461654 isomorphism types \cite{KreherRadziszowski87a} \cite{Schmalz}

---

# 7709: 5-(28,6,11)

• clan: 21-(44,22,11), 16 times derived
• $PSL(2,27)$ 28068645 isomorphism types \cite{KreherRadziszowski87a} \cite{Schmalz}
• $PSU(3,9)$ many isomorphism types
• derived from 6-(29,7,11) (# 11992)

---

# 7710: 5-(28,6,12)

• clan: 21-(44,22,12), 16 times derived
• $PSU(3,9)$ many isomorphism types
• derived from supplementary of 6-(29,7,11) (# 11992)

---

# 7711: 5-(28,6,2)

• clan: 21-(44,22,2), 16 times derived
• $PGL(2,13)\times C_2$ 11 solutions
• $PSL(2,27)$ 20 isomorphism types \cite{KreherRadziszowski87a} \cite{Schmalz}

---

# 7712: 5-(28,6,3)

• clan: 21-(44,22,3), 16 times derived
• $PSL(2,27)$ 695 isomorphism types \cite{KreherRadziszowski87a}\cite{Schmalz}

---

# 7713: 5-(28,6,4)

• clan: 21-(44,22,4), 16 times derived
• $PSL(2,27)$ 6132 isomorphism types \cite{KreherRadziszowski87a}\cite{Schmalz}

---

# 7714: 5-(28,6,5)

• clan: 21-(44,22,5), 16 times derived
• $PSL(2,27)$ 74882 isomorphism types \cite{KreherRadziszowski87a}\cite{Schmalz}
• $PSU(3,9)$ 5724 isomorphism types

---

# 7715: 5-(28,6,6)

• clan: 21-(44,22,6), 16 times derived
• $PSL(2,27)$ 370650 isomorphism types \cite{KreherRadziszowski87a}\cite{Schmalz}
• $PSU(3,9)$ 5290 isomorphism types

---

# 7716: 5-(28,6,7)

• clan: 21-(44,22,7), 16 times derived
• $PSL(2,27)$ 1707742 isomorphism types \cite{KreherRadziszowski87a}\cite{Schmalz}

---

# 7717: 5-(28,6,8)

• clan: 21-(44,22,8), 16 times derived
• $PSL(2,27)$ 5710925 isomorphism types \cite{KreherRadziszowski87a}\cite{Schmalz}
• $PSU(3,9)$ 539278 isomorphism types

---

# 7718: 5-(28,6,9)

• clan: 21-(44,22,9), 16 times derived
• $PSL(2,27)$ 11496089 isomorphism types \cite{KreherRadziszowski87a}\cite{Schmalz}
• $PSU(3,9)$ many isomorphism types

---

# 7719: 5-(28,7,1)

• clan: 8-(31,10,1), 3 times derived
• Steiner system ! $PGL(2,27)$ (1 isom. type) \cite{Denniston76}

---

# 7720: 5-(28,7,30)

• clan: 8-(31,10,30), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 15000}$

---

# 7721: 5-(28,7,33)

• clan: 21-(44,22,3), 15 times derived, 1 times residual
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$

---

# 7722: 5-(29,7,36)

• clan: 21-(44,22,3), 1 times reduced t, 15 times derived
• Tran van Trung construction (left) for 5-(28,7,33) (# 7721) : der= 5-(28,6,3) and res= 5-(28,7,33) - the given design is the residual.

---

# 7723: 5-(28,7,40)

• clan: 8-(31,10,40), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$

---

# 7724: 5-(28,7,43)

• clan: 8-(31,10,43), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$
• $ {\bf P\Gamma L(2,27)} 49$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,43) (# 12029)

---

# 7725: 5-(28,7,60)

• clan: 8-(31,10,60), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$

---

# 7726: 5-(28,7,63)

• clan: 8-(31,10,63), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$
• $ {\bf P\Gamma L(2,27)} 385$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,63) (# 12041)
• derived from supplementary of 6-(29,8,190) (# 16059)

---

# 7727: 5-(28,7,70)

• clan: 8-(31,10,70), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$
• $ {\bf P\Gamma L(2,27)} 702$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,70) (# 12049)

---

# 7728: 5-(28,7,73)

• clan: 8-(31,10,73), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$

---

# 7729: 5-(28,7,90)

• clan: 8-(31,10,90), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$

---

# 7730: 5-(28,7,93)

• clan: 8-(31,10,93), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$
• $S_8^{[2]}$ (1 isom. type)
• derived from 6-(29,8,93) (# 18023)
• derived from supplementary of 6-(29,8,160) (# 18025)

---

# 7731: 5-(28,7,100)

• clan: 8-(31,10,100), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$
• derived from 6-(29,8,100) (# 18006)
• derived from supplementary of 6-(29,8,153) (# 18008)

---

# 7732: 5-(28,7,103)

• clan: 8-(31,10,103), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$

---

# 7733: 5-(28,7,120)

• clan: 8-(31,10,120), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$
• $ {\bf P\Gamma L(2,27)} 4652$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,120) (# 12014)
• derived from supplementary of 6-(29,8,133) (# 12020)

---

# 7734: 5-(28,7,123)

• clan: 8-(31,10,123), 3 times derived
• $ {\bf P\Gamma L(2,25)\oplus C_2\ \ge 1}$
• $ {\bf C_2\times PSL(2,13)} \geq 1$

---

# 7735: 5-(28,7,105)

• clan: 8-(31,10,105), 3 times derived
• $ {\bf P\Gamma L(2,27)} 3055$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,105) (# 12003)
• derived from supplementary of 6-(29,8,148) (# 16048)

---

# 7736: 5-(28,7,106)

• clan: 8-(31,10,106), 3 times derived
• $ {\bf P\Gamma L(2,27)} 3055$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,106) (# 12007)

---

# 7737: 5-(28,7,112)

• clan: 8-(31,10,112), 3 times derived
• $ {\bf P\Gamma L(2,27)} 4926$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,112) (# 12011)
• derived from supplementary of 6-(29,8,141) (# 16053)

---

# 7738: 5-(28,7,113)

• clan: 8-(31,10,113), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7739: 5-(28,7,119)

• clan: 8-(31,10,119), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7740: 5-(28,7,126)

• clan: 8-(31,10,126), 3 times derived
• $ {\bf P\Gamma L(2,27)} 3580$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,126) (# 12017)

---

# 7741: 5-(28,7,14)

• clan: 8-(31,10,14), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7742: 5-(28,7,15)

• clan: 8-(31,10,15), 3 times derived
• $ {\bf P\Gamma L(2,27)} 1$ % -group 3 PGGL 2 27 PGGL_2_27

---

# 7743: 5-(28,7,21)

• clan: 8-(31,10,21), 3 times derived
• $ {\bf P\Gamma L(2,27)} 10$ % -group 3 PGGL 2 27 PGGL_2_27

---

# 7744: 5-(28,7,22)

• clan: 21-(44,22,2), 15 times derived, 1 times residual
• $ {\bf P\Gamma L(2,27)} 10$ % -group 3 PGGL 2 27 PGGL_2_27

---

# 7745: 5-(29,7,24)

• clan: 21-(44,22,2), 1 times reduced t, 15 times derived
• Tran van Trung construction (left) for 5-(28,7,22) (# 7744) : der= 5-(28,6,2) and res= 5-(28,7,22) - the given design is the residual.
• $PGL(2,27)+$ (>=1 isom. types)

---

# 7746: 5-(28,7,28)

• clan: 8-(31,10,28), 3 times derived
• $ {\bf P\Gamma L(2,27)} 10$ % -group 3 PGGL 2 27 PGGL_2_27

---

# 7747: 5-(28,7,29)

• clan: 8-(31,10,29), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7748: 5-(28,7,35)

• clan: 8-(31,10,35), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7749: 5-(28,7,36)

• clan: 8-(31,10,36), 3 times derived
• $ {\bf P\Gamma L(2,27)} 24$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,36) (# 12021)

---

# 7750: 5-(28,7,42)

• clan: 8-(31,10,42), 3 times derived
• $ {\bf P\Gamma L(2,27)} 49$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,42) (# 12025)

---

# 7751: 5-(28,7,49)

• clan: 8-(31,10,49), 3 times derived
• $ {\bf P\Gamma L(2,27)} 215$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,49) (# 12033)

---

# 7752: 5-(28,7,50)

• clan: 8-(31,10,50), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7753: 5-(28,7,56)

• clan: 8-(31,10,56), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7754: 5-(28,7,57)

• clan: 8-(31,10,57), 3 times derived
• $ {\bf P\Gamma L(2,27)} 332$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,57) (# 12037)

---

# 7755: 5-(28,7,64)

• clan: 8-(31,10,64), 3 times derived
• $ {\bf P\Gamma L(2,27)} 385$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,64) (# 12045)
• derived from supplementary of 6-(29,8,189) (# 16066)

---

# 7756: 5-(28,7,7)

• clan: 8-(31,10,7), 3 times derived
• $ {\bf PSL(2,27)} $ (2 isom. types) % -group 3 PSL 2 27 PSL_2_27

---

# 7757: 5-(28,7,71)

• clan: 8-(31,10,71), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7758: 5-(28,7,77)

• clan: 21-(44,22,7), 15 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7759: 5-(29,7,84)

• clan: 21-(44,22,7), 1 times reduced t, 15 times derived
• Tran van Trung construction (left) for 5-(28,7,77) (# 7758) : der= 5-(28,6,7) and res= 5-(28,7,77) - the given design is the residual.
• $PGL(2,27)+$ (>=1 isom. types)

---

# 7760: 5-(28,7,78)

• clan: 8-(31,10,78), 3 times derived
• $ {\bf P\Gamma L(2,27)} 1298$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,78) (# 12053)

---

# 7761: 5-(28,7,8)

• clan: 8-(31,10,8), 3 times derived
• $ {\bf PSL(2,27)} $ (2 isom. types) % -group 3 PSL 2 27 PSL_2_27

---

# 7762: 5-(28,7,84)

• clan: 8-(31,10,84), 3 times derived
• $ {\bf P\Gamma L(2,27)} 1634$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,84) (# 12057)

---

# 7763: 5-(28,7,85)

• clan: 8-(31,10,85), 3 times derived
• $ {\bf P\Gamma L(2,27)} 1634$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,85) (# 12061)

---

# 7764: 5-(28,7,88)

• clan: 21-(44,22,8), 15 times derived, 1 times residual
• $ {\bf PSL(2,13)\times C_2}$

---

# 7765: 5-(29,7,96)

• clan: 21-(44,22,8), 1 times reduced t, 15 times derived
• Tran van Trung construction (left) for 5-(28,7,88) (# 7764) : der= 5-(28,6,8) and res= 5-(28,7,88) - the given design is the residual.

---

# 7766: 5-(28,7,91)

• clan: 8-(31,10,91), 3 times derived
• $ {\bf P\Gamma L(2,27)} 1579$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,91) (# 12065)

---

# 7767: 5-(28,7,92)

• clan: 9-(31,10,8), 1 times reduced t, 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7768: 5-(28,7,98)

• clan: 8-(31,10,98), 3 times derived
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7769: 5-(28,7,99)

• clan: 21-(44,22,9), 15 times derived, 1 times residual
• $ {\bf P\Gamma L(2,27)} 1929$ % -group 3 PGGL 2 27 PGGL_2_27
• derived from 6-(29,8,99) (# 12069)

---

# 7770: 5-(29,7,108)

• clan: 21-(44,22,9), 1 times reduced t, 15 times derived
• Tran van Trung construction (left) for 5-(28,7,99) (# 7769) : der= 5-(28,6,9) and res= 5-(28,7,99) - the given design is the residual.
• $PGL(2,27)+$ (>=1 isom. types)
• derived from 6-(30,8,108) (# 12282)

---

# 7771: 5-(28,8,1001)

• clan: 21-(44,22,13), 14 times derived, 2 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7772: 5-(28,8,105)

• clan: 8-(31,10,15), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
• derived from 6-(29,9,105) (# 12073)

---

# 7773: 5-(29,8,120)

• clan: 8-(31,10,15), 1 times reduced t, 2 times derived
• Tran van Trung construction (left) for 5-(28,8,105) (# 7772) : der= 5-(28,7,15) and res= 5-(28,8,105) - the given design is the residual.

---

# 7774: 5-(28,8,112)

• clan: 8-(31,10,16), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7775: 5-(28,8,119)

• clan: 8-(31,10,17), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7776: 5-(28,8,126)

• clan: 8-(31,10,18), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
• derived from 6-(29,9,126) (# 12077)

---

# 7777: 5-(28,8,133)

• clan: 8-(31,10,19), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7778: 5-(28,8,140)

• clan: 8-(31,10,20), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7779: 5-(28,8,147)

• clan: 8-(31,10,21), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7780: 5-(29,8,168)

• clan: 8-(31,10,21), 1 times reduced t, 2 times derived
• Tran van Trung construction (left) for 5-(28,8,147) (# 7779) : der= 5-(28,7,21) and res= 5-(28,8,147) - the given design is the residual.

---

# 7781: 5-(28,8,154)

• clan: 21-(44,22,2), 14 times derived, 2 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27
• derived from 6-(29,9,154) (# 12081)

---

# 7782: 5-(29,8,176)

• clan: 21-(44,22,2), 1 times reduced t, 14 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(28,8,154) (# 7781) : der= 5-(28,7,22) and res= 5-(28,8,154) - the given design is the residual.

---

# 7783: 5-(30,8,200)

• clan: 21-(44,22,2), 2 times reduced t, 14 times derived
• Tran van Trung construction (left) for 5-(29,8,176) (# 7782) : der= 5-(29,7,24) and res= 5-(29,8,176) - the given design is the residual.
• derived from 6-(31,9,200) (# 12296)

---

# 7784: 5-(28,8,161)

• clan: 9-(31,10,2), 1 times reduced t, 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7785: 5-(28,8,168)

• clan: 8-(31,10,24), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7786: 5-(28,8,175)

• clan: 8-(31,10,25), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7787: 5-(28,8,182)

• clan: 8-(31,10,26), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7788: 5-(28,8,189)

• clan: 8-(31,10,27), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7789: 5-(28,8,196)

• clan: 8-(31,10,28), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7790: 5-(29,8,224)

• clan: 8-(31,10,28), 1 times reduced t, 2 times derived
• Tran van Trung construction (left) for 5-(28,8,196) (# 7789) : der= 5-(28,7,28) and res= 5-(28,8,196) - the given design is the residual.

---

# 7791: 5-(28,8,203)

• clan: 8-(31,10,29), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7792: 5-(29,8,232)

• clan: 8-(31,10,29), 1 times reduced t, 2 times derived
• Tran van Trung construction (left) for 5-(28,8,203) (# 7791) : der= 5-(28,7,29) and res= 5-(28,8,203) - the given design is the residual.

---

# 7793: 5-(28,8,21)

• clan: 8-(31,10,3), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7794: 5-(28,8,210)

• clan: 8-(31,10,30), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7795: 5-(29,8,240)

• clan: 8-(31,10,30), 1 times reduced t, 2 times derived
• Tran van Trung construction (left) for 5-(28,8,210) (# 7794) : der= 5-(28,7,30) and res= 5-(28,8,210) - the given design is the residual.

---

# 7796: 5-(28,8,217)

• clan: 8-(31,10,31), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7797: 5-(28,8,224)

• clan: 8-(31,10,32), 2 times derived, 1 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7798: 5-(28,8,231)

• clan: 21-(44,22,3), 14 times derived, 2 times residual
• $ {\bf PSL(2,27)} \geq 1$ % -group 3 PSL 2 27 PSL_2_27

---

# 7799: 5-(29,8,264)

• clan: 21-(44,22,3), 1 times reduced t, 14 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(28,8,231) (# 7798) : der= 5-(28,7,33) and res= 5-(28,8,231) - the given design is the residual.

---

---

created: Fri Oct 23 11:11:32 CEST 2009