Best Known (47−33, 47, s)-Nets in Base 256
(47−33, 47, 271)-Net over F256 — Constructive and digital
Digital (14, 47, 271)-net over F256, using
- net from sequence [i] based on digital (14, 270)-sequence over F256, using
(47−33, 47, 513)-Net over F256 — Digital
Digital (14, 47, 513)-net over F256, using
- t-expansion [i] based on digital (8, 47, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
(47−33, 47, 223704)-Net in Base 256 — Upper bound on s
There is no (14, 47, 223705)-net in base 256, because
- 1 times m-reduction [i] would yield (14, 46, 223705)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 601 269616 036192 846781 329142 138484 712030 061216 836288 616517 031413 915912 312746 695089 050271 855159 763440 860113 192651 > 25646 [i]