Best Known (31−27, 31, s)-Nets in Base 128
(31−27, 31, 192)-Net over F128 — Constructive and digital
Digital (4, 31, 192)-net over F128, using
- t-expansion [i] based on digital (3, 31, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
(31−27, 31, 215)-Net over F128 — Digital
Digital (4, 31, 215)-net over F128, using
- net from sequence [i] based on digital (4, 214)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 4 and N(F) ≥ 215, using
(31−27, 31, 257)-Net in Base 128 — Constructive
(4, 31, 257)-net in base 128, using
- 1 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- base change [i] based on digital (0, 28, 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, 28, 257)-net over F256, using
(31−27, 31, 3247)-Net in Base 128 — Upper bound on s
There is no (4, 31, 3248)-net in base 128, because
- 1 times m-reduction [i] would yield (4, 30, 3248)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 1647 288725 393321 269298 475381 956145 304718 081570 806600 857956 583411 > 12830 [i]