MinT - Best Known (28, 28+12, s)-Nets in Base 8

Best Known (28, 28+12, s)-Nets in Base 8

(28, 28+12, 354)-Net over F₈ — Constructive and digital

Digital (28, 40, 354)-net over F₈, using

2 times m-reduction [i] based on digital (28, 42, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 21, 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]

(28, 28+12, 531)-Net in Base 8 — Constructive

(28, 40, 531)-net in base 8, using

base change [i] based on digital (18, 30, 531)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 6, 17)-net over F₁₆, using
    - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
        the rational function field F₁₆(x) [i]
      - Niederreiter sequence [i]
  2. digital (12, 24, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 12, 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]

(28, 28+12, 1354)-Net over F₈ — Digital

Digital (28, 40, 1354)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 28+12, 448456)-Net in Base 8 — Upper bound on s

There is no (28, 40, 448457)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 329229 876952 268667 328719 602764 543420 > 8⁴⁰ [i]