Best Known (1, 1+5, s)-Nets in Base 128
(1, 1+5, 150)-Net over F128 — Constructive and digital
Digital (1, 6, 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
(1, 1+5, 257)-Net in Base 128 — Constructive
(1, 6, 257)-net in base 128, using
- 2 times m-reduction [i] based on (1, 8, 257)-net in base 128, using
- base change [i] based on digital (0, 7, 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
- base change [i] based on digital (0, 7, 257)-net over F256, using
(1, 1+5, 2063)-Net in Base 128 — Upper bound on s
There is no (1, 6, 2064)-net in base 128, because
- 1 times m-reduction [i] would yield (1, 5, 2064)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 34372 713577 > 1285 [i]