MinT - Best Known (40, 40+31, s)-Nets in Base 9

Best Known (40, 40+31, s)-Nets in Base 9

(40, 40+31, 300)-Net over F₉ — Constructive and digital

Digital (40, 71, 300)-net over F₉, using

1 times m-reduction [i] based on digital (40, 72, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 36, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(40, 40+31, 308)-Net over F₉ — Digital

Digital (40, 71, 308)-net over F₉, using

1 times m-reduction [i] based on digital (40, 72, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 36, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(40, 40+31, 22784)-Net in Base 9 — Upper bound on s

There is no (40, 71, 22785)-net in base 9, because

1 times m-reduction [i] would yield (40, 70, 22785)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 267903 856685 652220 496404 156660 324694 264104 784547 067463 628758 683833 > 9⁷⁰ [i]