Best Known (63−34, 63, s)-Nets in Base 9
(63−34, 63, 78)-Net over F9 — Constructive and digital
Digital (29, 63, 78)-net over F9, using
- t-expansion [i] based on digital (22, 63, 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
(63−34, 63, 84)-Net in Base 9 — Constructive
(29, 63, 84)-net in base 9, using
- base change [i] based on digital (8, 42, 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
(63−34, 63, 110)-Net over F9 — Digital
Digital (29, 63, 110)-net over F9, using
- t-expansion [i] based on digital (26, 63, 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
(63−34, 63, 3074)-Net in Base 9 — Upper bound on s
There is no (29, 63, 3075)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 315449 426090 836714 603487 058910 745610 030040 346664 669237 579161 > 963 [i]