Best Known (78−72, 78, s)-Nets in Base 81
(78−72, 78, 160)-Net over F81 — Constructive and digital
Digital (6, 78, 160)-net over F81, using
- t-expansion [i] based on digital (5, 78, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(78−72, 78, 190)-Net over F81 — Digital
Digital (6, 78, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(78−72, 78, 2361)-Net in Base 81 — Upper bound on s
There is no (6, 78, 2362)-net in base 81, because
- 14 times m-reduction [i] would yield (6, 64, 2362)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 139 459899 586666 572872 011284 532748 715307 115615 541739 159484 989145 632335 736004 348617 776556 338314 777709 997049 945763 062008 027041 > 8164 [i]