MinT - Best Known (17, 17+47, s)-Nets in Base 256

Best Known (17, 17+47, s)-Nets in Base 256

(17, 17+47, 274)-Net over F₂₅₆ — Constructive and digital

Digital (17, 64, 274)-net over F₂₅₆, using

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

(17, 17+47, 513)-Net over F₂₅₆ — Digital

Digital (17, 64, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 64, 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, 17+47, 146004)-Net in Base 256 — Upper bound on s

There is no (17, 64, 146005)-net in base 256, because

1 times m-reduction [i] would yield (17, 63, 146005)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 52 377668 671490 557221 561628 169443 123498 195663 581415 932349 635422 958212 636782 602341 141257 146892 221599 512146 086651 138217 817528 151551 177832 426637 391561 168576 > 256⁶³ [i]