Best Known (17−13, 17, s)-Nets in Base 64
(17−13, 17, 104)-Net over F64 — Constructive and digital
Digital (4, 17, 104)-net over F64, using
- t-expansion [i] based on digital (3, 17, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
(17−13, 17, 129)-Net over F64 — Digital
Digital (4, 17, 129)-net over F64, using
- net from sequence [i] based on digital (4, 128)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
(17−13, 17, 150)-Net in Base 64 — Constructive
(4, 17, 150)-net in base 64, using
- 4 times m-reduction [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
(17−13, 17, 3111)-Net in Base 64 — Upper bound on s
There is no (4, 17, 3112)-net in base 64, because
- 1 times m-reduction [i] would yield (4, 16, 3112)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 79272 040126 271674 849676 214175 > 6416 [i]