MinT - Best Known (8, 8+49, s)-Nets in Base 256

Best Known (8, 8+49, s)-Nets in Base 256

(8, 8+49, 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
- Niederreiter sequence [i]

(8, 8+49, 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
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
  - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(8, 8+49, 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 256^mÂ â‰¥ 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]