MinT - Best Known (71, 71+25, s)-Nets in Base 8

Best Known (71, 71+25, s)-Nets in Base 8

(71, 71+25, 562)-Net over F₈ — Constructive and digital

Digital (71, 96, 562)-net over F₈, using

8² times duplication [i] based on digital (69, 94, 562)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (18, 30, 208)-net over F₈, using
    - trace code for nets [i] based on digital (3, 15, 104)-net over F₆₄, using
      - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]
  2. digital (39, 64, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 32, 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]

(71, 71+25, 772)-Net in Base 8 — Constructive

(71, 96, 772)-net in base 8, using

(u,Â u+v)-construction [i] based on
1. (16, 28, 258)-net in base 8, using
  - trace code for nets [i] based on (2, 14, 129)-net in base 64, using
    - base change [i] based on digital (0, 12, 129)-net over F₁₂₈, using
      - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]
2. (43, 68, 514)-net in base 8, using
  - base change [i] based on digital (26, 51, 514)-net over F₁₆, using
    - 1 times m-reduction [i] based on digital (26, 52, 514)-net over F₁₆, using
      - trace code for nets [i] based on digital (0, 26, 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]

(71, 71+25, 5748)-Net over F₈ — Digital

Digital (71, 96, 5748)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+25, large)-Net in Base 8 — Upper bound on s

There is no (71, 96, large)-net in base 8, because

23 times m-reduction [i] would yield (71, 73, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]