MinT - Best Known (80, 80+26, s)-Nets in Base 8

Best Known (80, 80+26, s)-Nets in Base 8

(80, 80+26, 708)-Net over F₈ — Constructive and digital

Digital (80, 106, 708)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (27, 40, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 20, 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]
2. digital (40, 66, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 33, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄ (see above)

(80, 80+26, 1028)-Net in Base 8 — Constructive

(80, 106, 1028)-net in base 8, using

8² times duplication [i] based on (78, 104, 1028)-net in base 8, using
- base change [i] based on digital (52, 78, 1028)-net over F₁₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (13, 26, 514)-net over F₁₆, using
      - trace code for nets [i] based on digital (0, 13, 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 (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 (see above)

(80, 80+26, 9821)-Net over F₈ — Digital

Digital (80, 106, 9821)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+26, large)-Net in Base 8 — Upper bound on s

There is no (80, 106, large)-net in base 8, because

24 times m-reduction [i] would yield (80, 82, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]