MinT - Best Known (147−38, 147, s)-Nets in Base 9

Best Known (147−38, 147, s)-Nets in Base 9

(147−38, 147, 904)-Net over F₉ — Constructive and digital

Digital (109, 147, 904)-net over F₉, using

1 times m-reduction [i] based on digital (109, 148, 904)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (19, 38, 164)-net over F₉, using
    - trace code for nets [i] based on digital (0, 19, 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 (71, 110, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 55, 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]

(147−38, 147, 11342)-Net over F₉ — Digital

Digital (109, 147, 11342)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−38, 147, large)-Net in Base 9 — Upper bound on s

There is no (109, 147, large)-net in base 9, because

36 times m-reduction [i] would yield (109, 111, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]