MinT - Best Known (149−40, 149, s)-Nets in Base 9

Best Known (149−40, 149, s)-Nets in Base 9

(149−40, 149, 814)-Net over F₉ — Constructive and digital

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]

(149−40, 149, 8531)-Net over F₉ — Digital

Digital (109, 149, 8531)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−40, 149, large)-Net in Base 9 — Upper bound on s

There is no (109, 149, large)-net in base 9, because

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