Best Known (45−45, 45, s)-Nets in Base 128
(45−45, 45, 129)-Net over F128 — Constructive and digital
Digital (0, 45, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
(45−45, 45, 129)-Net in Base 128 — Upper bound on s
There is no (0, 45, 130)-net in base 128, because
- 43 times m-reduction [i] would yield (0, 2, 130)-net in base 128, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 128m ≥ 16511 > 1282 [i]