MinT - Best Known (125−33, 125, s)-Nets in Base 9

Best Known (125−33, 125, s)-Nets in Base 9

(125−33, 125, 780)-Net over F₉ — Constructive and digital

Digital (92, 125, 780)-net over F₉, using

2 times m-reduction [i] based on digital (92, 127, 780)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (8, 25, 40)-net over F₉, using
    - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
        a function field by SÃ©mirat [i]
  2. digital (67, 102, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 51, 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]

(125−33, 125, 788)-Net in Base 9 — Constructive

(92, 125, 788)-net in base 9, using

(u,Â u+v)-construction [i] based on
1. (11, 27, 48)-net in base 9, using
  - base change [i] based on digital (2, 18, 48)-net over F₂₇, using
    - net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
        a function field by GarcÃa and Quoos [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]

(125−33, 125, 8553)-Net over F₉ — Digital

Digital (92, 125, 8553)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−33, 125, large)-Net in Base 9 — Upper bound on s

There is no (92, 125, large)-net in base 9, because

31 times m-reduction [i] would yield (92, 94, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]