MinT - Best Known (150−40, 150, s)-Nets in Base 9

Best Known (150−40, 150, s)-Nets in Base 9

(150−40, 150, 814)-Net over F₉ — Constructive and digital

Digital (110, 150, 814)-net over F₉, using

9¹ times duplication [i] based on digital (109, 149, 814)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 37, 74)-net over F₉, using
    - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
        a function field by GarcÃa and Quoos [i]
  2. digital (72, 112, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 56, 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]

(150−40, 150, 9025)-Net over F₉ — Digital

Digital (110, 150, 9025)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−40, 150, large)-Net in Base 9 — Upper bound on s

There is no (110, 150, large)-net in base 9, because

38 times m-reduction [i] would yield (110, 112, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]