MinT - Best Known (77, 107, s)-Nets in Base 16

Best Known (77, 107, s)-Nets in Base 16

(77, 107, 1093)-Net over F₁₆ — Constructive and digital

Digital (77, 107, 1093)-net over F₁₆, using

1 times m-reduction [i] based on digital (77, 108, 1093)-net over F₁₆, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (6, 16, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]
  2. 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]
  3. digital (31, 62, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 31, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(77, 107, 21583)-Net over F₁₆ — Digital

Digital (77, 107, 21583)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 107, large)-Net in Base 16 — Upper bound on s

There is no (77, 107, large)-net in base 16, because

28 times m-reduction [i] would yield (77, 79, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]