MinT - Best Known (144−38, 144, s)-Nets in Base 9

Best Known (144−38, 144, s)-Nets in Base 9

(144−38, 144, 814)-Net over F₉ — Constructive and digital

Digital (106, 144, 814)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (17, 36, 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 (70, 108, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 54, 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]

(144−38, 144, 9494)-Net over F₉ — Digital

Digital (106, 144, 9494)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−38, 144, large)-Net in Base 9 — Upper bound on s

There is no (106, 144, large)-net in base 9, because

36 times m-reduction [i] would yield (106, 108, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]