MinT - Best Known (14, 14+45, s)-Nets in Base 256

Best Known (14, 14+45, s)-Nets in Base 256

(14, 14+45, 271)-Net over F₂₅₆ — Constructive and digital

Digital (14, 59, 271)-net over F₂₅₆, using

net from sequence [i] based on digital (14, 270)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(14, 14+45, 513)-Net over F₂₅₆ — Digital

Digital (14, 59, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 59, 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]

(14, 14+45, 79295)-Net in Base 256 — Upper bound on s

There is no (14, 59, 79296)-net in base 256, because

1 times m-reduction [i] would yield (14, 58, 79296)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 47 634431 011704 644592 181624 964713 934460 770861 107755 224942 129800 291037 379494 326020 590637 427725 633769 747657 386140 388576 939910 115494 577684 066461 > 256⁵⁸ [i]