MinT - Best Known (129−42, 129, s)-Nets in Base 16

Best Known (129−42, 129, s)-Nets in Base 16

(129−42, 129, 1030)-Net over F₁₆ — Constructive and digital

Digital (87, 129, 1030)-net over F₁₆, using

1 times m-reduction [i] based on digital (87, 130, 1030)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 42, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 21, 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 (45, 88, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 44, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(129−42, 129, 6633)-Net over F₁₆ — Digital

Digital (87, 129, 6633)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−42, 129, large)-Net in Base 16 — Upper bound on s

There is no (87, 129, large)-net in base 16, because

40 times m-reduction [i] would yield (87, 89, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]