Best Known (31, 149, s)-Nets in Base 9
(31, 149, 78)-Net over F9 — Constructive and digital
Digital (31, 149, 78)-net over F9, using
- t-expansion [i] based on digital (22, 149, 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, 149, 120)-Net over F9 — Digital
Digital (31, 149, 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, 149, 697)-Net in Base 9 — Upper bound on s
There is no (31, 149, 698)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 16272 534942 852292 736193 727481 668917 460025 756467 574462 800321 755048 498752 660394 895060 089975 825730 126597 673101 535630 294261 488733 182456 165734 020913 > 9149 [i]