Best Known (31, 31+58, s)-Nets in Base 9
(31, 31+58, 78)-Net over F9 — Constructive and digital
Digital (31, 89, 78)-net over F9, using
- t-expansion [i] based on digital (22, 89, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(31, 31+58, 120)-Net over F9 — Digital
Digital (31, 89, 120)-net over F9, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
(31, 31+58, 1220)-Net in Base 9 — Upper bound on s
There is no (31, 89, 1221)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8 661125 314228 048217 908480 532781 471386 203761 986794 405834 535511 077960 389481 510964 574473 > 989 [i]