MinT - Best Known (128−42, 128, s)-Nets in Base 16

Best Known (128−42, 128, s)-Nets in Base 16

(128−42, 128, 1030)-Net over F₁₆ — Constructive and digital

Digital (86, 128, 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 (44, 86, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 43, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(128−42, 128, 6201)-Net over F₁₆ — Digital

Digital (86, 128, 6201)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−42, 128, large)-Net in Base 16 — Upper bound on s

There is no (86, 128, large)-net in base 16, because

40 times m-reduction [i] would yield (86, 88, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]