MinT - Best Known (24, 24+35, s)-Nets in Base 256

Best Known (24, 24+35, s)-Nets in Base 256

(24, 24+35, 521)-Net over F₂₅₆ — Constructive and digital

Digital (24, 59, 521)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 20, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 39, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(24, 24+35, 1025)-Net over F₂₅₆ — Digital

Digital (24, 59, 1025)-net over F₂₅₆, using

net from sequence [i] based on digital (24, 1024)-sequence over F₂₅₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 24 and N(F) ≥ 1025, using
  - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(24, 24+35, 4631827)-Net in Base 256 — Upper bound on s

There is no (24, 59, 4631828)-net in base 256, because

1 times m-reduction [i] would yield (24, 58, 4631828)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 47 634171 320371 437601 297228 250492 153722 409091 197873 361889 697686 617659 426510 523546 036355 008694 566600 434166 301419 476808 476338 535495 636838 939781 > 256⁵⁸ [i]