Best Known (56−30, 56, s)-Nets in Base 9
(56−30, 56, 78)-Net over F9 — Constructive and digital
Digital (26, 56, 78)-net over F9, using
- t-expansion [i] based on digital (22, 56, 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
(56−30, 56, 82)-Net in Base 9 — Constructive
(26, 56, 82)-net in base 9, using
- 1 times m-reduction [i] based on (26, 57, 82)-net in base 9, using
- base change [i] based on digital (7, 38, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- base change [i] based on digital (7, 38, 82)-net over F27, using
(56−30, 56, 110)-Net over F9 — Digital
Digital (26, 56, 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
(56−30, 56, 2923)-Net in Base 9 — Upper bound on s
There is no (26, 56, 2924)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 274938 315513 059878 217822 565953 426493 794811 980988 415521 > 956 [i]