Best Known (5, 5+17, s)-Nets in Base 64
(5, 5+17, 128)-Net over F64 — Constructive and digital
Digital (5, 22, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
(5, 5+17, 133)-Net over F64 — Digital
Digital (5, 22, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
(5, 5+17, 150)-Net in Base 64 — Constructive
(5, 22, 150)-net in base 64, using
- 6 times m-reduction [i] based on (5, 28, 150)-net in base 64, using
- base change [i] based on digital (1, 24, 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, 24, 150)-net over F128, using
(5, 5+17, 3289)-Net in Base 64 — Upper bound on s
There is no (5, 22, 3290)-net in base 64, because
- 1 times m-reduction [i] would yield (5, 21, 3290)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 85 231117 715419 465558 186966 842372 645295 > 6421 [i]