MinT - Best Known (81, 110, s)-Nets in Base 8

Best Known (81, 110, s)-Nets in Base 8

(81, 110, 610)-Net over F₈ — Constructive and digital

Digital (81, 110, 610)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (24, 38, 256)-net over F₈, using
  - trace code for nets [i] based on digital (5, 19, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]
2. digital (43, 72, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 36, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(81, 110, 708)-Net in Base 8 — Constructive

(81, 110, 708)-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. digital (43, 72, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 36, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(81, 110, 5712)-Net over F₈ — Digital

Digital (81, 110, 5712)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 110, large)-Net in Base 8 — Upper bound on s

There is no (81, 110, large)-net in base 8, because

27 times m-reduction [i] would yield (81, 83, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]