MinT - Best Known (89, 118, s)-Nets in Base 8

Best Known (89, 118, s)-Nets in Base 8

(89, 118, 1026)-Net over F₈ — Constructive and digital

Digital (89, 118, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (89, 122, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 61, 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]

(89, 118, 1030)-Net in Base 8 — Constructive

(89, 118, 1030)-net in base 8, using

(u,Â u+v)-construction [i] based on
1. (24, 38, 514)-net in base 8, using
  - trace code for nets [i] based on (5, 19, 257)-net in base 64, using
    - 1 times m-reduction [i] based on (5, 20, 257)-net in base 64, using
      - base change [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. (51, 80, 516)-net in base 8, using
  - base change [i] based on digital (31, 60, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 30, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(89, 118, 10336)-Net over F₈ — Digital

Digital (89, 118, 10336)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 118, large)-Net in Base 8 — Upper bound on s

There is no (89, 118, large)-net in base 8, because

27 times m-reduction [i] would yield (89, 91, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]