Best Known (26, 26+28, s)-Nets in Base 9
(26, 26+28, 78)-Net over F9 — Constructive and digital
Digital (26, 54, 78)-net over F9, using
- t-expansion [i] based on digital (22, 54, 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
(26, 26+28, 84)-Net in Base 9 — Constructive
(26, 54, 84)-net in base 9, using
- base change [i] based on digital (8, 36, 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
(26, 26+28, 110)-Net over F9 — Digital
Digital (26, 54, 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
(26, 26+28, 3614)-Net in Base 9 — Upper bound on s
There is no (26, 54, 3615)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 3390 142834 567546 781564 078787 354157 535628 938638 590353 > 954 [i]