MinT - Best Known (14, 14+51, s)-Nets in Base 256

Best Known (14, 14+51, s)-Nets in Base 256

(14, 14+51, 271)-Net over F₂₅₆ — Constructive and digital

Digital (14, 65, 271)-net over F₂₅₆, using

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

(14, 14+51, 513)-Net over F₂₅₆ — Digital

Digital (14, 65, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 65, 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+51, 58356)-Net in Base 256 — Upper bound on s

There is no (14, 65, 58357)-net in base 256, because

1 times m-reduction [i] would yield (14, 64, 58357)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 13410 139750 487892 813015 881707 590598 307556 544347 453752 445047 088577 530156 064211 232575 331015 044218 134031 890796 957884 135738 589593 677456 044826 113110 964666 323376 > 256⁶⁴ [i]