MinT - Best Known (125−31, 125, s)-Nets in Base 9

Best Known (125−31, 125, s)-Nets in Base 9

(125−31, 125, 904)-Net over F₉ — Constructive and digital

Digital (94, 125, 904)-net over F₉, using

9¹ times duplication [i] based on digital (93, 124, 904)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 30, 164)-net over F₉, using
    - trace code for nets [i] based on digital (0, 15, 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 (63, 94, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 47, 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]

(125−31, 125, 14261)-Net over F₉ — Digital

Digital (94, 125, 14261)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−31, 125, large)-Net in Base 9 — Upper bound on s

There is no (94, 125, large)-net in base 9, because

29 times m-reduction [i] would yield (94, 96, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]