Best Known (66−36, 66, s)-Nets in Base 9
(66−36, 66, 78)-Net over F9 — Constructive and digital
Digital (30, 66, 78)-net over F9, using
- t-expansion [i] based on digital (22, 66, 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
(66−36, 66, 84)-Net in Base 9 — Constructive
(30, 66, 84)-net in base 9, using
- base change [i] based on digital (8, 44, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(66−36, 66, 110)-Net over F9 — Digital
Digital (30, 66, 110)-net over F9, using
- t-expansion [i] based on digital (26, 66, 110)-net over F9, using
- net from sequence [i] based on digital (26, 109)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 26 and N(F) ≥ 110, using
- net from sequence [i] based on digital (26, 109)-sequence over F9, using
(66−36, 66, 2967)-Net in Base 9 — Upper bound on s
There is no (30, 66, 2968)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 959 093551 758912 171634 739390 787477 980335 664237 221126 051579 611265 > 966 [i]