MinT - Best Known (58−39, 58, s)-Nets in Base 256

Best Known (58−39, 58, s)-Nets in Base 256

(58−39, 58, 514)-Net over F₂₅₆ — Constructive and digital

Digital (19, 58, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 19, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]
2. digital (0, 39, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(58−39, 58, 521660)-Net in Base 256 — Upper bound on s

There is no (19, 58, 521661)-net in base 256, because

1 times m-reduction [i] would yield (19, 57, 521661)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 186076 430712 457350 097078 506267 940559 824412 266387 981921 591187 503150 618383 408777 234107 901732 138897 749843 939440 423198 923995 207865 121502 430196 > 256⁵⁷ [i]