Best Known (18−18, 18, s)-Nets in Base 64
(18−18, 18, 65)-Net over F64 — Constructive and digital
Digital (0, 18, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
(18−18, 18, 65)-Net in Base 64 — Upper bound on s
There is no (0, 18, 66)-net in base 64, because
- 16 times m-reduction [i] would yield (0, 2, 66)-net in base 64, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 64m ≥ 4159 > 642 [i]