MinT - Best Known (17, 58, s)-Nets in Base 256

Best Known (17, 58, s)-Nets in Base 256

(17, 58, 274)-Net over F₂₅₆ — Constructive and digital

Digital (17, 58, 274)-net over F₂₅₆, using

net from sequence [i] based on digital (17, 273)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(17, 58, 513)-Net over F₂₅₆ — Digital

Digital (17, 58, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 58, 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]

(17, 58, 237811)-Net in Base 256 — Upper bound on s

There is no (17, 58, 237812)-net in base 256, because

1 times m-reduction [i] would yield (17, 57, 237812)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 186081 900701 682536 980828 985857 181553 343190 074787 036303 678617 666069 437829 490897 749113 524173 032477 537080 017043 179426 603755 217038 194018 653576 > 256⁵⁷ [i]