MinT - Best Known (94, 124, s)-Nets in Base 8

Best Known (94, 124, s)-Nets in Base 8

(94, 124, 1026)-Net over F₈ — Constructive and digital

Digital (94, 124, 1026)-net over F₈, using

8 times m-reduction [i] based on digital (94, 132, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 66, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(94, 124, 1030)-Net in Base 8 — Constructive

(94, 124, 1030)-net in base 8, using

base change [i] based on 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]

(94, 124, 12135)-Net over F₈ — Digital

Digital (94, 124, 12135)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 124, large)-Net in Base 8 — Upper bound on s

There is no (94, 124, large)-net in base 8, because

28 times m-reduction [i] would yield (94, 96, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]