MinT - Best Known (99−32, 99, s)-Nets in Base 16

Best Known (99−32, 99, s)-Nets in Base 16

(99−32, 99, 1030)-Net over F₁₆ — Constructive and digital

Digital (67, 99, 1030)-net over F₁₆, using

1 times m-reduction [i] based on digital (67, 100, 1030)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (16, 32, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 16, 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 (35, 68, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 34, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(99−32, 99, 5814)-Net over F₁₆ — Digital

Digital (67, 99, 5814)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−32, 99, large)-Net in Base 16 — Upper bound on s

There is no (67, 99, large)-net in base 16, because

30 times m-reduction [i] would yield (67, 69, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]