Best Known (3, 3+11, s)-Nets in Base 64
(3, 3+11, 104)-Net over F64 — Constructive and digital
Digital (3, 14, 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+11, 113)-Net over F64 — Digital
Digital (3, 14, 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+11, 150)-Net in Base 64 — Constructive
(3, 14, 150)-net in base 64, using
- base change [i] based on digital (1, 12, 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
(3, 3+11, 2051)-Net in Base 64 — Upper bound on s
There is no (3, 14, 2052)-net in base 64, because
- 1 times m-reduction [i] would yield (3, 13, 2052)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 302417 558174 571610 438144 > 6413 [i]