Best Known (17, 17+33, s)-Nets in Base 256
(17, 17+33, 515)-Net over F256 — Constructive and digital
Digital (17, 50, 515)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 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
- digital (1, 34, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (0, 16, 257)-net over F256, using
(17, 17+33, 546)-Net over F256 — Digital
Digital (17, 50, 546)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 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
- digital (1, 34, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- digital (0, 16, 257)-net over F256, using
(17, 17+33, 632744)-Net in Base 256 — Upper bound on s
There is no (17, 50, 632745)-net in base 256, because
- 1 times m-reduction [i] would yield (17, 49, 632745)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 10087 090044 449372 683526 138435 867235 349660 539850 042823 934665 231581 504867 525822 391339 612233 171948 099497 378020 857542 045226 > 25649 [i]