Best Known (3, 3+9, s)-Nets in Base 64
(3, 3+9, 104)-Net over F64 — Constructive and digital
Digital (3, 12, 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
(3, 3+9, 113)-Net over F64 — Digital
Digital (3, 12, 113)-net over F64, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
(3, 3+9, 257)-Net in Base 64 — Constructive
(3, 12, 257)-net in base 64, using
- base change [i] based on digital (0, 9, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(3, 3+9, 3254)-Net in Base 64 — Upper bound on s
There is no (3, 12, 3255)-net in base 64, because
- 1 times m-reduction [i] would yield (3, 11, 3255)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 73 822549 107221 736571 > 6411 [i]