Best Known (31, 31+80, s)-Nets in Base 9
(31, 31+80, 78)-Net over F9 — Constructive and digital
Digital (31, 111, 78)-net over F9, using
- t-expansion [i] based on digital (22, 111, 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+80, 120)-Net over F9 — Digital
Digital (31, 111, 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+80, 852)-Net in Base 9 — Upper bound on s
There is no (31, 111, 853)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8667 701673 518354 271527 826254 767127 750864 862190 319970 318749 557793 843507 149844 104485 132603 454982 607434 977089 > 9111 [i]