MinT - Best Known (137−37, 137, s)-Nets in Base 9

Best Known (137−37, 137, s)-Nets in Base 9

(137−37, 137, 804)-Net over F₉ — Constructive and digital

Digital (100, 137, 804)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 31, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]
2. digital (69, 106, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 53, 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]

(137−37, 137, 7657)-Net over F₉ — Digital

Digital (100, 137, 7657)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−37, 137, large)-Net in Base 9 — Upper bound on s

There is no (100, 137, large)-net in base 9, because

35 times m-reduction [i] would yield (100, 102, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]