MinT - Best Known (131−31, 131, s)-Nets in Base 9

Best Known (131−31, 131, s)-Nets in Base 9

(131−31, 131, 972)-Net over F₉ — Constructive and digital

Digital (100, 131, 972)-net over F₉, using

1 times m-reduction [i] based on digital (100, 132, 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 (64, 96, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 48, 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]

(131−31, 131, 22123)-Net over F₉ — Digital

Digital (100, 131, 22123)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−31, 131, large)-Net in Base 9 — Upper bound on s

There is no (100, 131, large)-net in base 9, because

29 times m-reduction [i] would yield (100, 102, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]