MinT - Best Known (138−36, 138, s)-Nets in Base 9

Best Known (138−36, 138, s)-Nets in Base 9

(138−36, 138, 804)-Net over F₉ — Constructive and digital

Digital (102, 138, 804)-net over F₉, using

2 times m-reduction [i] based on digital (102, 140, 804)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 32, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
        a function field by GarcÃa and Quoos [i]
  2. digital (70, 108, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 54, 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]

(138−36, 138, 10078)-Net over F₉ — Digital

Digital (102, 138, 10078)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−36, 138, large)-Net in Base 9 — Upper bound on s

There is no (102, 138, large)-net in base 9, because

34 times m-reduction [i] would yield (102, 104, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]