MinT - Best Known (127−31, 127, s)-Nets in Base 9

Best Known (127−31, 127, s)-Nets in Base 9

(127−31, 127, 940)-Net over F₉ — Constructive and digital

Digital (96, 127, 940)-net over F₉, using

9¹ times duplication [i] based on digital (95, 126, 940)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 32, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 16, 100)-net over F₈₁, using
      - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [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]

(127−31, 127, 16509)-Net over F₉ — Digital

Digital (96, 127, 16509)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−31, 127, large)-Net in Base 9 — Upper bound on s

There is no (96, 127, large)-net in base 9, because

29 times m-reduction [i] would yield (96, 98, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]