MinT - Best Known (90, 121, s)-Nets in Base 9

Best Known (90, 121, s)-Nets in Base 9

(90, 121, 788)-Net over F₉ — Constructive and digital

Digital (90, 121, 788)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (12, 27, 48)-net over F₉, using
  - (u,Â u+v)-construction [i] based on
    1. digital (2, 9, 20)-net over F₉, using
      - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
        a function field by GarcÃa and Quoos [i]
    2. digital (3, 18, 28)-net over F₉, using
      - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
        the Hermitian function field over F₉ [i]
2. digital (63, 94, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 47, 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]

(90, 121, 792)-Net in Base 9 — Constructive

(90, 121, 792)-net in base 9, using

(u,Â u+v)-construction [i] based on
1. (12, 27, 52)-net in base 9, using
  - base change [i] based on digital (3, 18, 52)-net over F₂₇, using
    - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
        a function field by SÃ©mirat [i]
2. digital (63, 94, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 47, 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]

(90, 121, 10643)-Net over F₉ — Digital

Digital (90, 121, 10643)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 121, large)-Net in Base 9 — Upper bound on s

There is no (90, 121, large)-net in base 9, because

29 times m-reduction [i] would yield (90, 92, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]