MinT - Best Known (137−35, 137, s)-Nets in Base 9

Best Known (137−35, 137, s)-Nets in Base 9

(137−35, 137, 904)-Net over F₉ — Constructive and digital

Digital (102, 137, 904)-net over F₉, using

9¹ times duplication [i] based on digital (101, 136, 904)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 34, 164)-net over F₉, using
    - trace code for nets [i] based on digital (0, 17, 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 (67, 102, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 51, 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]

(137−35, 137, 11859)-Net over F₉ — Digital

Digital (102, 137, 11859)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−35, 137, large)-Net in Base 9 — Upper bound on s

There is no (102, 137, large)-net in base 9, because

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