MinT - Best Known (139−38, 139, s)-Nets in Base 9

Best Known (139−38, 139, s)-Nets in Base 9

(139−38, 139, 780)-Net over F₉ — Constructive and digital

Digital (101, 139, 780)-net over F₉, using

3 times m-reduction [i] based on digital (101, 142, 780)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (8, 28, 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 (73, 114, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 57, 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]

(139−38, 139, 7060)-Net over F₉ — Digital

Digital (101, 139, 7060)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−38, 139, large)-Net in Base 9 — Upper bound on s

There is no (101, 139, large)-net in base 9, because

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