MinT - Best Known (63, 63+30, s)-Nets in Base 16

Best Known (63, 63+30, s)-Nets in Base 16

(63, 63+30, 1030)-Net over F₁₆ — Constructive and digital

Digital (63, 93, 1030)-net over F₁₆, using

1 times m-reduction [i] based on digital (63, 94, 1030)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 30, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 15, 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 (33, 64, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 32, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(63, 63+30, 5671)-Net over F₁₆ — Digital

Digital (63, 93, 5671)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+30, large)-Net in Base 16 — Upper bound on s

There is no (63, 93, large)-net in base 16, because

28 times m-reduction [i] would yield (63, 65, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]