Best Known (57−57, 57, s)-Nets in Base 16
(57−57, 57, 17)-Net over F16 — Constructive and digital
Digital (0, 57, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
(57−57, 57, 17)-Net in Base 16 — Upper bound on s
There is no (0, 57, 18)-net in base 16, because
- 55 times m-reduction [i] would yield (0, 2, 18)-net in base 16, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 16m ≥ 271 > 162 [i]