MinT - Best Known (133−32, 133, s)-Nets in Base 9

Best Known (133−32, 133, s)-Nets in Base 9

(133−32, 133, 972)-Net over F₉ — Constructive and digital

Digital (101, 133, 972)-net over F₉, using

1 times m-reduction [i] based on digital (101, 134, 972)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (20, 36, 232)-net over F₉, using
    - trace code for nets [i] based on digital (2, 18, 116)-net over F₈₁, using
      - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]
  2. digital (65, 98, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 49, 370)-net over F₈₁, using
      - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(133−32, 133, 19288)-Net over F₉ — Digital

Digital (101, 133, 19288)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−32, 133, large)-Net in Base 9 — Upper bound on s

There is no (101, 133, large)-net in base 9, because

30 times m-reduction [i] would yield (101, 103, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]