MinT - Best Known (64−34, 64, s)-Nets in Base 256

Best Known (64−34, 64, s)-Nets in Base 256

(64−34, 64, 773)-Net over F₂₅₆ — Constructive and digital

Digital (30, 64, 773)-net over F₂₅₆, using

1 times m-reduction [i] based on digital (30, 65, 773)-net over F₂₅₆, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 11, 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 (1, 18, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
  3. digital (1, 36, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(64−34, 64, 2434)-Net over F₂₅₆ — Digital

Digital (30, 64, 2434)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−34, 64, large)-Net in Base 256 — Upper bound on s

There is no (30, 64, large)-net in base 256, because

32 times m-reduction [i] would yield (30, 32, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]