MinT - Best Known (142−37, 142, s)-Nets in Base 9

Best Known (142−37, 142, s)-Nets in Base 9

(142−37, 142, 904)-Net over F₉ — Constructive and digital

Digital (105, 142, 904)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (18, 36, 164)-net over F₉, using
  - trace code for nets [i] based on digital (0, 18, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
2. digital (69, 106, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 53, 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]

(142−37, 142, 10384)-Net over F₉ — Digital

Digital (105, 142, 10384)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−37, 142, large)-Net in Base 9 — Upper bound on s

There is no (105, 142, large)-net in base 9, because

35 times m-reduction [i] would yield (105, 107, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]