Best Known (57−49, 57, s)-Nets in Base 256
(57−49, 57, 265)-Net over F256 — Constructive and digital
Digital (8, 57, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(57−49, 57, 513)-Net over F256 — Digital
Digital (8, 57, 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
(57−49, 57, 15985)-Net in Base 256 — Upper bound on s
There is no (8, 57, 15986)-net in base 256, because
- 1 times m-reduction [i] would yield (8, 56, 15986)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 727 059266 557602 505085 589518 508199 095116 605573 101453 479876 559256 167465 071535 803453 065974 513996 116412 730656 792656 646045 433071 871649 654596 > 25656 [i]