MinT - Best Known (54−36, 54, s)-Nets in Base 256

Best Known (54−36, 54, s)-Nets in Base 256

(54−36, 54, 514)-Net over F₂₅₆ — Constructive and digital

Digital (18, 54, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 18, 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, 36, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(54−36, 54, 496938)-Net in Base 256 — Upper bound on s

There is no (18, 54, 496939)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 11091 046341 159008 995324 989146 419920 946655 979367 472532 423958 350404 147523 285655 053216 299749 549486 888961 811632 175792 041291 597135 585386 > 256⁵⁴ [i]