t designs with small t, id ge 10500

---

# 10500: 6-(26,10,1575)

• clan: 13-(32,16,315), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,1575) (# 14006)

---

# 10501: 5-(26,10,13734)

• clan: 13-(32,16,654), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,1575) (# 10500) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,3270) (# 10502) : der= 5-(25,9,3270) and res= 5-(25,10,10464) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,10464) (# 10503) : der= 5-(25,9,3270) and res= 5-(25,10,10464) - the given design is the residual.
• derived from supplementary of 6-(27,11,6615) (# 10675)
• derived from 6-(27,11,13734) (# 14008)
• design 6-(26,10,3270) (# 14009) with respect to smaller t

---

# 10502: 5-(25,9,3270)

• clan: 13-(32,16,654), 1 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,1575) (# 10500)
• derived from 6-(26,10,3270) (# 14009)

---

# 10503: 5-(25,10,10464)

• clan: 13-(32,16,654), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,1575) (# 10500)
• derived from supplementary of 6-(26,11,5040) (# 14007)
• residual design of 6-(26,10,3270) (# 14009)
• derived from 6-(26,11,10464) (# 14010)

---

# 10504: 6-(26,10,1620)

• clan: 13-(32,16,324), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,1620) (# 14023)
• Tran van Trung construction (left) for 6-(25,10,1296) (# 17560) : der= 6-(25,9,324) and res= 6-(25,10,1296) - the given design is the residual.

---

# 10505: 5-(26,10,13545)

• clan: 13-(32,16,645), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,1620) (# 10504) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,10320) (# 10506) : der= 5-(25,9,3225) and res= 5-(25,10,10320) - the given design is the residual.
• derived from supplementary of 6-(27,11,6804) (# 10686)
• derived from 6-(27,11,13545) (# 14025)
• design 6-(26,10,3225) (# 14026) with respect to smaller t

---

# 10506: 5-(25,10,10320)

• clan: 13-(32,16,645), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,1620) (# 10504)
• derived from supplementary of 6-(26,11,5184) (# 14024)
• residual design of 6-(26,10,3225) (# 14026)
• derived from 6-(26,11,10320) (# 14027)
• supplementary design of 6-(25,10,1296) (# 17560) with respect to smaller t
• design 6-(25,10,2580) (# 17562) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,10,7740) (# 17566) : der= 5-(24,9,2580) and res= 5-(24,10,7740) - the given design is the residual.

---

# 10507: 6-(26,10,1650)

• clan: 13-(32,16,330), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,1650) (# 14030)

---

# 10508: 5-(26,10,13419)

• clan: 13-(32,16,639), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,1650) (# 10507) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,3195) (# 10509) : der= 5-(25,9,3195) and res= 5-(25,10,10224) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,10224) (# 10510) : der= 5-(25,9,3195) and res= 5-(25,10,10224) - the given design is the residual.
• derived from supplementary of 6-(27,11,6930) (# 14031)
• derived from 6-(27,11,13419) (# 14033)
• design 6-(26,10,3195) (# 14034) with respect to smaller t

---

# 10509: 5-(25,9,3195)

• clan: 13-(32,16,639), 1 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,1650) (# 10507)
• derived from 6-(26,10,3195) (# 14034)

---

# 10510: 5-(25,10,10224)

• clan: 13-(32,16,639), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,1650) (# 10507)
• derived from supplementary of 6-(26,11,5280) (# 14032)
• residual design of 6-(26,10,3195) (# 14034)
• derived from 6-(26,11,10224) (# 14035)

---

# 10511: 6-(26,10,1695)

• clan: 13-(32,16,339), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25

---

# 10512: 5-(26,10,13230)

• clan: 13-(32,16,630), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,1695) (# 10511) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,3150) (# 10513) : der= 5-(25,9,3150) and res= 5-(25,10,10080) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,10080) (# 10514) : der= 5-(25,9,3150) and res= 5-(25,10,10080) - the given design is the residual.
• derived from supplementary of 6-(27,11,7119) (# 13583)

---

# 10513: 5-(25,9,3150)

• clan: 13-(32,16,630), 1 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,1695) (# 10511)
• Tran van Trung construction (left) for 5-(24,9,2520) (# 13584) : der= 5-(24,8,630) and res= 5-(24,9,2520) - the given design is the residual.

---

# 10514: 5-(25,10,10080)

• clan: 13-(32,16,630), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,1695) (# 10511)
• derived from supplementary of 6-(26,11,5424) (# 13573)
• supplementary design of 6-(25,10,1356) (# 13574) with respect to smaller t
• derived from 6-(26,11,10080) (# 13576)
• design 6-(25,10,2520) (# 13577) with respect to smaller t
• Tran van Trung construction (right) for 5-(24,9,2520) (# 13584) : der= 5-(24,9,2520) and res= 5-(24,10,7560) - the given design is the derived.
• Tran van Trung construction (left) for 5-(24,10,7560) (# 13585) : der= 5-(24,9,2520) and res= 5-(24,10,7560) - the given design is the residual.

---

# 10515: 6-(26,10,1800)

• clan: 13-(32,16,360), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25

---

# 10516: 5-(26,10,12789)

• clan: 13-(32,16,609), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,1800) (# 10515) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,9744) (# 10517) : der= 5-(25,9,3045) and res= 5-(25,10,9744) - the given design is the residual.

---

# 10517: 5-(25,10,9744)

• clan: 13-(32,16,609), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,1800) (# 10515)

---

# 10518: 6-(26,10,1845)

• clan: 13-(32,16,369), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,1845) (# 14103)

---

# 10519: 5-(26,10,12600)

• clan: 13-(32,16,600), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,1845) (# 10518) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,9600) (# 10520) : der= 5-(25,9,3000) and res= 5-(25,10,9600) - the given design is the residual.
• derived from supplementary of 6-(27,11,7749) (# 10712)
• derived from 6-(27,11,12600) (# 14105)
• design 6-(26,10,3000) (# 14106) with respect to smaller t

---

# 10520: 5-(25,10,9600)

• clan: 13-(32,16,600), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,1845) (# 10518)
• derived from supplementary of 6-(26,11,5904) (# 14104)
• residual design of 6-(26,10,3000) (# 14106)
• derived from 6-(26,11,9600) (# 14107)

---

# 10521: 6-(26,10,1875)

• clan: 13-(32,16,375), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,1875) (# 14126)

---

# 10522: 5-(26,10,12474)

• clan: 13-(32,16,594), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,1875) (# 10521) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,9504) (# 10523) : der= 5-(25,9,2970) and res= 5-(25,10,9504) - the given design is the residual.
• derived from supplementary of 6-(27,11,7875) (# 14127)
• derived from 6-(27,11,12474) (# 14129)
• design 6-(26,10,2970) (# 14130) with respect to smaller t

---

# 10523: 5-(25,10,9504)

• clan: 13-(32,16,594), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,1875) (# 10521)
• derived from supplementary of 6-(26,11,6000) (# 14128)
• residual design of 6-(26,10,2970) (# 14130)
• derived from 6-(26,11,9504) (# 14131)

---

# 10524: 6-(26,10,2295)

• clan: 17-(36,18,9), 1 times reduced t, 8 times derived, 2 times residual
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• residual design of 7-(27,10,540) (# 13794)
• derived from 7-(27,11,2295) (# 14308)

---

# 10525: 5-(26,10,10710)

• clan: 17-(36,18,10), 2 times reduced t, 8 times derived, 2 times residual
• supplementary design of 6-(26,10,2295) (# 10524) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,2550) (# 10526) : der= 5-(25,9,2550) and res= 5-(25,10,8160) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,8160) (# 10527) : der= 5-(25,9,2550) and res= 5-(25,10,8160) - the given design is the residual.
• residual design of supplementary of 6-(27,10,2835) (# 10589)
• residual design of 6-(27,10,3150) (# 10600)
• derived from supplementary of 6-(27,11,9639) (# 10759)
• design 6-(26,10,2550) (# 13795) with respect to smaller t
• derived from 6-(27,11,10710) (# 14310)

---

# 10526: 5-(25,9,2550)

• clan: 17-(36,18,10), 1 times reduced t, 9 times derived, 2 times residual
• derived from supplementary of 6-(26,10,2295) (# 10524)
• residual design of supplementary of 6-(26,9,540) (# 10588)
• residual design of 6-(26,9,600) (# 10594)
• supplementary design of 6-(25,9,459) (# 13782) with respect to smaller t
• design 6-(25,9,510) (# 13784) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,9,2040) (# 13785) : der= 5-(24,8,510) and res= 5-(24,9,2040) - the given design is the residual.
• derived from 6-(26,10,2550) (# 13795)

---

# 10527: 5-(25,10,8160)

• clan: 17-(36,18,10), 1 times reduced t, 8 times derived, 3 times residual
• residual design of supplementary of 6-(26,10,2295) (# 10524)
• residual design of 6-(26,10,2550) (# 13795)
• derived from supplementary of 6-(26,11,7344) (# 14309)
• derived from 6-(26,11,8160) (# 14311)

---

# 10528: 5-(26,9,3150)

• clan: 17-(36,18,10), 2 times reduced t, 9 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(25,9,2550) (# 10526) : der= 5-(25,8,600) and res= 5-(25,9,2550) - the given design is the residual.
• supplementary design of 6-(26,9,540) (# 10588) with respect to smaller t
• derived from supplementary of 6-(27,10,2835) (# 10589)
• design 6-(26,9,600) (# 10594) with respect to smaller t
• derived from 6-(27,10,3150) (# 10600)
• residual design of supplementary of 6-(27,9,630) (# 15114)
• residual design of 6-(27,9,700) (# 15116)

---

# 10529: 5-(27,10,13860)

• clan: 17-(36,18,10), 3 times reduced t, 8 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(26,9,3150) (# 10528) : der= 5-(26,9,3150) and res= 5-(26,10,10710) - the given design is the derived.
• supplementary design of 6-(27,10,2835) (# 10589) with respect to smaller t
• design 6-(27,10,3150) (# 10600) with respect to smaller t
• derived from supplementary of 6-(28,11,12474) (# 10764)
• derived from 6-(28,11,13860) (# 14315)
• residual design of supplementary of 6-(28,10,3465) (# 15113)
• residual design of 6-(28,10,3850) (# 15115)

---

# 10530: 6-(26,10,2325)

• clan: 13-(32,16,465), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,2325) (# 14316)

---

# 10531: 5-(26,10,10584)

• clan: 13-(32,16,504), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,2325) (# 10530) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,8064) (# 10532) : der= 5-(25,9,2520) and res= 5-(25,10,8064) - the given design is the residual.
• derived from supplementary of 6-(27,11,9765) (# 10768)
• derived from 6-(27,11,10584) (# 14318)
• design 6-(26,10,2520) (# 14319) with respect to smaller t

---

# 10532: 5-(25,10,8064)

• clan: 13-(32,16,504), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,2325) (# 10530)
• derived from supplementary of 6-(26,11,7440) (# 14317)
• residual design of 6-(26,10,2520) (# 14319)
• derived from 6-(26,11,8064) (# 14320)

---

# 10533: 6-(26,10,570)

• clan: 15-(32,16,2), 3 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25

---

# 10534: 5-(26,10,17955)

• clan: 15-(32,16,15), 4 times reduced t, 6 times derived
• supplementary design of 6-(26,10,570) (# 10533) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,4275) (# 10535) : der= 5-(25,9,4275) and res= 5-(25,10,13680) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,13680) (# 10536) : der= 5-(25,9,4275) and res= 5-(25,10,13680) - the given design is the residual.

---

# 10535: 5-(25,9,4275)

• clan: 15-(32,16,15), 3 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,570) (# 10533)

---

# 10536: 5-(25,10,13680)

• clan: 15-(32,16,15), 3 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,570) (# 10533)

---

# 10537: 6-(26,10,675)

• clan: 13-(32,16,135), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,675) (# 14372)

---

# 10538: 5-(26,10,17514)

• clan: 13-(32,16,834), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,675) (# 10537) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,4170) (# 10539) : der= 5-(25,9,4170) and res= 5-(25,10,13344) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,13344) (# 10540) : der= 5-(25,9,4170) and res= 5-(25,10,13344) - the given design is the residual.
• derived from supplementary of 6-(27,11,2835) (# 14373)
• derived from 6-(27,11,17514) (# 14375)
• design 6-(26,10,4170) (# 14376) with respect to smaller t

---

# 10539: 5-(25,9,4170)

• clan: 13-(32,16,834), 1 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,675) (# 10537)
• derived from 6-(26,10,4170) (# 14376)

---

# 10540: 5-(25,10,13344)

• clan: 13-(32,16,834), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,675) (# 10537)
• derived from supplementary of 6-(26,11,2160) (# 14374)
• residual design of 6-(26,10,4170) (# 14376)
• derived from 6-(26,11,13344) (# 14377)

---

# 10541: 6-(26,10,720)

• clan: 13-(32,16,144), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25

---

# 10542: 5-(26,10,17325)

• clan: 13-(32,16,825), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,720) (# 10541) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,13200) (# 10543) : der= 5-(25,9,4125) and res= 5-(25,10,13200) - the given design is the residual.

---

# 10543: 5-(25,10,13200)

• clan: 13-(32,16,825), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,720) (# 10541)

---

# 10544: 6-(26,10,750)

• clan: 13-(32,16,150), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25

---

# 10545: 5-(26,10,17199)

• clan: 13-(32,16,819), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,750) (# 10544) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,4095) (# 10546) : der= 5-(25,9,4095) and res= 5-(25,10,13104) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,13104) (# 10547) : der= 5-(25,9,4095) and res= 5-(25,10,13104) - the given design is the residual.

---

# 10546: 5-(25,9,4095)

• clan: 13-(32,16,819), 1 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,750) (# 10544)

---

# 10547: 5-(25,10,13104)

• clan: 13-(32,16,819), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,750) (# 10544)

---

# 10548: 6-(26,10,795)

• clan: 13-(32,16,159), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25

---

# 10549: 5-(26,10,17010)

• clan: 13-(32,16,810), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,795) (# 10548) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,4050) (# 10550) : der= 5-(25,9,4050) and res= 5-(25,10,12960) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,12960) (# 10551) : der= 5-(25,9,4050) and res= 5-(25,10,12960) - the given design is the residual.
• derived from supplementary of 6-(27,11,3339) (# 14590)

---

# 10550: 5-(25,9,4050)

• clan: 13-(32,16,810), 1 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,795) (# 10548)

---

# 10551: 5-(25,10,12960)

• clan: 13-(32,16,810), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,795) (# 10548)
• derived from supplementary of 6-(26,11,2544) (# 14583)
• derived from 6-(26,11,12960) (# 14586)

---

# 10552: 6-(26,10,900)

• clan: 13-(32,16,180), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,900) (# 14478)

---

# 10553: 5-(26,10,16569)

• clan: 13-(32,16,789), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,900) (# 10552) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,12624) (# 10554) : der= 5-(25,9,3945) and res= 5-(25,10,12624) - the given design is the residual.
• derived from supplementary of 6-(27,11,3780) (# 14479)
• derived from 6-(27,11,16569) (# 14481)
• design 6-(26,10,3945) (# 14482) with respect to smaller t

---

# 10554: 5-(25,10,12624)

• clan: 13-(32,16,789), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,900) (# 10552)
• derived from supplementary of 6-(26,11,2880) (# 14480)
• residual design of 6-(26,10,3945) (# 14482)
• derived from 6-(26,11,12624) (# 14483)

---

# 10555: 6-(26,10,945)

• clan: 13-(32,16,189), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25
• derived from 7-(27,11,945) (# 14506)

---

# 10556: 5-(26,10,16380)

• clan: 13-(32,16,780), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,945) (# 10555) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,12480) (# 10557) : der= 5-(25,9,3900) and res= 5-(25,10,12480) - the given design is the residual.
• derived from supplementary of 6-(27,11,3969) (# 14507)
• derived from 6-(27,11,16380) (# 14509)
• design 6-(26,10,3900) (# 14510) with respect to smaller t

---

# 10557: 5-(25,10,12480)

• clan: 13-(32,16,780), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,945) (# 10555)
• derived from supplementary of 6-(26,11,3024) (# 14508)
• residual design of 6-(26,10,3900) (# 14510)
• derived from 6-(26,11,12480) (# 14511)

---

# 10558: 6-(26,10,975)

• clan: 13-(32,16,195), 1 times reduced t, 6 times derived
• $ {\bf PGL(2,25)} \geq 1$ % -group 3 PGL 2 25 PGL_2_25

---

# 10559: 5-(26,10,16254)

• clan: 13-(32,16,774), 2 times reduced t, 6 times derived
• supplementary design of 6-(26,10,975) (# 10558) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,9,3870) (# 10560) : der= 5-(25,9,3870) and res= 5-(25,10,12384) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,10,12384) (# 10561) : der= 5-(25,9,3870) and res= 5-(25,10,12384) - the given design is the residual.

---

# 10560: 5-(25,9,3870)

• clan: 13-(32,16,774), 1 times reduced t, 7 times derived
• derived from supplementary of 6-(26,10,975) (# 10558)

---

# 10561: 5-(25,10,12384)

• clan: 13-(32,16,774), 1 times reduced t, 6 times derived, 1 times residual
• residual design of supplementary of 6-(26,10,975) (# 10558)

---

# 10562: 6-(26,8,60)

• clan: 17-(36,18,6), 1 times reduced t, 10 times derived
• $P\Gamma L(2,25)$ (23 isomorphism types) \cite{Sebille98} \cite{Bettenetal97b}
• design 7-(26,8,6) (# 13762) with respect to smaller t
• Tran van Trung construction (right) for 6-(25,7,6) (# 13763) : der= 6-(25,7,6) and res= 6-(25,8,54) - the given design is the derived.
• derived from 7-(27,9,60) (# 13772)

---

# 10563: 5-(26,8,910)

• clan: 17-(36,18,13), 2 times reduced t, 10 times derived
• supplementary design of 6-(26,8,60) (# 10562) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,7,130) (# 10564) : der= 5-(25,7,130) and res= 5-(25,8,780) - the given design is the derived.
• derived from supplementary of 6-(27,9,420) (# 10578)
• design 6-(26,8,130) (# 13764) with respect to smaller t
• derived from 6-(27,9,910) (# 13774)

---

# 10564: 5-(25,7,130)

• clan: 17-(36,18,13), 1 times reduced t, 11 times derived
• derived from supplementary of 6-(26,8,60) (# 10562)
• supplementary design of 6-(25,7,6) (# 13763) with respect to smaller t
• derived from 6-(26,8,130) (# 13764)
• design 6-(25,7,13) (# 13765) with respect to smaller t
• Tran van Trung construction (right) for 5-(24,6,13) (# 13767) : der= 5-(24,6,13) and res= 5-(24,7,117) - the given design is the derived.

---

# 10565: 6-(26,8,70)

• clan: 17-(36,18,7), 1 times reduced t, 10 times derived
• $P\Gamma L(2,25)$ (87 isomorphism types) \cite{Bettenetal97b}

---

# 10566: 5-(26,8,840)

• clan: 17-(36,18,12), 2 times reduced t, 10 times derived
• supplementary design of 6-(26,8,70) (# 10565) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,7,120) (# 10567) : der= 5-(25,7,120) and res= 5-(25,8,720) - the given design is the derived.
• derived from supplementary of 6-(27,9,490) (# 10583)

---

# 10567: 5-(25,7,120)

• clan: 17-(36,18,12), 1 times reduced t, 11 times derived
• derived from supplementary of 6-(26,8,70) (# 10565)

---

# 10568: 6-(26,9,180)

• clan: 17-(36,18,3), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 1$ % -group 3 PSL 2 25 PSL_2_25

---

# 10569: 5-(26,9,5040)

• clan: 17-(36,18,16), 2 times reduced t, 9 times derived, 1 times residual
• supplementary design of 6-(26,9,180) (# 10568) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,8,960) (# 10570) : der= 5-(25,8,960) and res= 5-(25,9,4080) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,9,4080) (# 10571) : der= 5-(25,8,960) and res= 5-(25,9,4080) - the given design is the residual.
• derived from supplementary of 6-(27,10,945) (# 10602)

---

# 10570: 5-(25,8,960)

• clan: 17-(36,18,16), 1 times reduced t, 10 times derived, 1 times residual
• derived from supplementary of 6-(26,9,180) (# 10568)

---

# 10571: 5-(25,9,4080)

• clan: 17-(36,18,16), 1 times reduced t, 9 times derived, 2 times residual
• residual design of supplementary of 6-(26,9,180) (# 10568)
• derived from supplementary of 6-(26,10,765) (# 14386)
• derived from 6-(26,10,4080) (# 14389)

---

# 10572: 6-(26,9,300)

• clan: 17-(36,18,5), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 1$ % -group 3 PSL 2 25 PSL_2_25

---

# 10573: 5-(26,9,4410)

• clan: 17-(36,18,14), 2 times reduced t, 9 times derived, 1 times residual
• supplementary design of 6-(26,9,300) (# 10572) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,9,3570) (# 10574) : der= 5-(25,8,840) and res= 5-(25,9,3570) - the given design is the residual.

---

# 10574: 5-(25,9,3570)

• clan: 17-(36,18,14), 1 times reduced t, 9 times derived, 2 times residual
• residual design of supplementary of 6-(26,9,300) (# 10572)

---

# 10575: 6-(26,9,360)

• clan: 17-(36,18,6), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 1$ % -group 3 PSL 2 25 PSL_2_25
• design 7-(26,9,54) (# 13768) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,9,306) (# 13769) : der= 6-(25,8,54) and res= 6-(25,9,306) - the given design is the residual.
• residual design of 7-(27,9,60) (# 13772)

---

# 10576: 5-(26,9,4095)

• clan: 17-(36,18,13), 2 times reduced t, 9 times derived, 1 times residual
• supplementary design of 6-(26,9,360) (# 10575) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,9,3315) (# 10577) : der= 5-(25,8,780) and res= 5-(25,9,3315) - the given design is the residual.
• residual design of supplementary of 6-(27,9,420) (# 10578)
• design 6-(26,9,780) (# 13770) with respect to smaller t
• residual design of 6-(27,9,910) (# 13774)

---

# 10577: 5-(25,9,3315)

• clan: 17-(36,18,13), 1 times reduced t, 9 times derived, 2 times residual
• residual design of supplementary of 6-(26,9,360) (# 10575)
• supplementary design of 6-(25,9,306) (# 13769) with respect to smaller t
• residual design of 6-(26,9,780) (# 13770)
• design 6-(25,9,663) (# 13771) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,9,2652) (# 13773) : der= 5-(24,8,663) and res= 5-(24,9,2652) - the given design is the residual.

---

# 10578: 6-(27,9,420)

• clan: 17-(36,18,6), 2 times reduced t, 9 times derived
• Tran van Trung construction (left) for 6-(26,9,360) (# 10575) : der= 6-(26,8,60) and res= 6-(26,9,360) - the given design is the residual.
• design 7-(27,9,60) (# 13772) with respect to smaller t

---

# 10579: 5-(27,9,5005)

• clan: 17-(36,18,13), 3 times reduced t, 9 times derived
• Tran van Trung construction (left) for 5-(26,9,4095) (# 10576) : der= 5-(26,8,910) and res= 5-(26,9,4095) - the given design is the residual.
• supplementary design of 6-(27,9,420) (# 10578) with respect to smaller t
• design 6-(27,9,910) (# 13774) with respect to smaller t
• derived from supplementary of 6-(28,10,2310) (# 15840)
• derived from 6-(28,10,5005) (# 15843)

---

# 10580: 6-(26,9,420)

• clan: 17-(36,18,7), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 1$ % -group 3 PSL 2 25 PSL_2_25
• design 7-(26,9,63) (# 13775) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,9,357) (# 13776) : der= 6-(25,8,63) and res= 6-(25,9,357) - the given design is the residual.
• derived from 7-(27,10,420) (# 13790)

---

# 10581: 5-(26,9,3780)

• clan: 17-(36,18,12), 2 times reduced t, 9 times derived, 1 times residual
• supplementary design of 6-(26,9,420) (# 10580) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,9,3060) (# 10582) : der= 5-(25,8,720) and res= 5-(25,9,3060) - the given design is the residual.
• residual design of supplementary of 6-(27,9,490) (# 10583)
• derived from supplementary of 6-(27,10,2205) (# 10595)
• derived from 6-(27,10,3780) (# 10601)
• design 6-(26,9,720) (# 13777) with respect to smaller t

---

# 10582: 5-(25,9,3060)

• clan: 17-(36,18,12), 1 times reduced t, 9 times derived, 2 times residual
• residual design of supplementary of 6-(26,9,420) (# 10580)
• supplementary design of 6-(25,9,357) (# 13776) with respect to smaller t
• residual design of 6-(26,9,720) (# 13777)
• design 6-(25,9,612) (# 13779) with respect to smaller t
• Tran van Trung construction (left) for 5-(24,9,2448) (# 13780) : der= 5-(24,8,612) and res= 5-(24,9,2448) - the given design is the residual.
• derived from supplementary of 6-(26,10,1785) (# 13791)
• derived from 6-(26,10,3060) (# 13792)

---

# 10583: 6-(27,9,490)

• clan: 17-(36,18,7), 2 times reduced t, 9 times derived
• Tran van Trung construction (left) for 6-(26,9,420) (# 10580) : der= 6-(26,8,70) and res= 6-(26,9,420) - the given design is the residual.
• \cite{Sebille98} $P\Gamma L(2,25)$

---

# 10584: 5-(27,9,4620)

• clan: 17-(36,18,12), 3 times reduced t, 9 times derived
• Tran van Trung construction (left) for 5-(26,9,3780) (# 10581) : der= 5-(26,8,840) and res= 5-(26,9,3780) - the given design is the residual.
• supplementary design of 6-(27,9,490) (# 10583) with respect to smaller t
• derived from supplementary of 6-(28,10,2695) (# 10598)

---

# 10585: 6-(26,9,480)

• clan: 17-(36,18,8), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 1$ % -group 3 PSL 2 25 PSL_2_25

---

# 10586: 5-(26,9,3465)

• clan: 17-(36,18,11), 2 times reduced t, 9 times derived, 1 times residual
• supplementary design of 6-(26,9,480) (# 10585) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,9,2805) (# 10587) : der= 5-(25,8,660) and res= 5-(25,9,2805) - the given design is the residual.

---

# 10587: 5-(25,9,2805)

• clan: 17-(36,18,11), 1 times reduced t, 9 times derived, 2 times residual
• residual design of supplementary of 6-(26,9,480) (# 10585)

---

# 10588: 6-(26,9,540)

• clan: 17-(36,18,9), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 24020080$ % -group 3 PSL 2 25 PSL_2_25
• $ {\bf C_2\times PSL(3,3)} \geq 1326387$ solutions %
• design 7-(26,9,81) (# 13781) with respect to smaller t
• Tran van Trung construction (left) for 6-(25,9,459) (# 13782) : der= 6-(25,8,81) and res= 6-(25,9,459) - the given design is the residual.
• derived from 7-(27,10,540) (# 13794)

---

# 10589: 6-(27,10,2835)

• clan: 17-(36,18,9), 2 times reduced t, 8 times derived, 1 times residual
• Tran van Trung construction (right) for 6-(26,9,540) (# 10588) : der= 6-(26,9,540) and res= 6-(26,10,2295) - the given design is the derived.
• \cite{Sebille98} $AGL(3,3)$
• design 7-(27,10,540) (# 13794) with respect to smaller t
• derived from 7-(28,11,2835) (# 14312)
• residual design of 7-(28,10,630) (# 15112)

---

# 10590: 6-(26,9,60)

• clan: 17-(36,18,1), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 1$ % -group 3 PSL 2 25 PSL_2_25

---

# 10591: 5-(26,9,5670)

• clan: 17-(36,18,18), 2 times reduced t, 9 times derived, 1 times residual
• supplementary design of 6-(26,9,60) (# 10590) with respect to smaller t
• Tran van Trung construction (right) for 5-(25,8,1080) (# 10592) : der= 5-(25,8,1080) and res= 5-(25,9,4590) - the given design is the derived.
• Tran van Trung construction (left) for 5-(25,9,4590) (# 10593) : der= 5-(25,8,1080) and res= 5-(25,9,4590) - the given design is the residual.

---

# 10592: 5-(25,8,1080)

• clan: 17-(36,18,18), 1 times reduced t, 10 times derived, 1 times residual
• derived from supplementary of 6-(26,9,60) (# 10590)

---

# 10593: 5-(25,9,4590)

• clan: 17-(36,18,18), 1 times reduced t, 9 times derived, 2 times residual
• residual design of supplementary of 6-(26,9,60) (# 10590)

---

# 10594: 6-(26,9,600)

• clan: 17-(36,18,10), 1 times reduced t, 9 times derived, 1 times residual
• $ {\bf PSL(2,25)} \geq 1$ % -group 3 PSL 2 25 PSL_2_25
• supplementary design of 7-(26,9,81) (# 13781) with respect to smaller t
• Tran van Trung construction (right) for 6-(25,8,90) (# 13783) : der= 6-(25,8,90) and res= 6-(25,9,510) - the given design is the derived.
• Tran van Trung construction (left) for 6-(25,9,510) (# 13784) : der= 6-(25,8,90) and res= 6-(25,9,510) - the given design is the residual.
• derived from supplementary of 7-(27,10,540) (# 13794)

---

# 10595: 6-(27,10,2205)

• clan: 17-(36,18,7), 2 times reduced t, 8 times derived, 1 times residual
• \cite{Sebille98} $AGL(3,3)$
• design 7-(27,10,420) (# 13790) with respect to smaller t
• Tran van Trung construction (left) for 6-(26,10,1785) (# 13791) : der= 6-(26,9,420) and res= 6-(26,10,1785) - the given design is the residual.
• derived from 7-(28,11,2205) (# 14099)

---

# 10596: 5-(27,10,16632)

• clan: 17-(36,18,12), 3 times reduced t, 8 times derived, 1 times residual
• supplementary design of 6-(27,10,2205) (# 10595) with respect to smaller t
• Tran van Trung construction (left) for 5-(26,10,12852) (# 10597) : der= 5-(26,9,3780) and res= 5-(26,10,12852) - the given design is the residual.
• residual design of supplementary of 6-(28,10,2695) (# 10598)
• design 6-(27,10,3780) (# 10601) with respect to smaller t
• derived from supplementary of 6-(28,11,9702) (# 10706)
• derived from 6-(28,11,16632) (# 14102)

---

# 10597: 5-(26,10,12852)

• clan: 17-(36,18,12), 2 times reduced t, 8 times derived, 2 times residual
• residual design of supplementary of 6-(27,10,2205) (# 10595)
• residual design of 6-(27,10,3780) (# 10601)
• derived from supplementary of 6-(27,11,7497) (# 10701)
• supplementary design of 6-(26,10,1785) (# 13791) with respect to smaller t
• design 6-(26,10,3060) (# 13792) with respect to smaller t
• Tran van Trung construction (left) for 5-(25,10,9792) (# 13793) : der= 5-(25,9,3060) and res= 5-(25,10,9792) - the given design is the residual.
• derived from 6-(27,11,12852) (# 14097)

---

# 10598: 6-(28,10,2695)

• clan: 17-(36,18,7), 3 times reduced t, 8 times derived
• Tran van Trung construction (left) for 6-(27,10,2205) (# 10595) : der= 6-(27,9,490) and res= 6-(27,10,2205) - the given design is the residual.

---

# 10599: 5-(28,10,21252)

• clan: 17-(36,18,12), 4 times reduced t, 8 times derived
• Tran van Trung construction (left) for 5-(27,10,16632) (# 10596) : der= 5-(27,9,4620) and res= 5-(27,10,16632) - the given design is the residual.
• supplementary design of 6-(28,10,2695) (# 10598) with respect to smaller t
• derived from supplementary of 6-(29,11,12397) (# 10709)

---

---

created: Fri Oct 23 11:12:30 CEST 2009