MinT - Best Known (40, 40+28, s)-Nets in Base 9

Best Known (40, 40+28, s)-Nets in Base 9

(40, 40+28, 320)-Net over F₉ — Constructive and digital

Digital (40, 68, 320)-net over F₉, using

2 times m-reduction [i] based on digital (40, 70, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 35, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(40, 40+28, 380)-Net over F₉ — Digital

Digital (40, 68, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 34, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(40, 40+28, 32594)-Net in Base 9 — Upper bound on s

There is no (40, 68, 32595)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 77357 756159 552544 112832 989307 270348 748762 038910 902508 294054 985425 > 9⁶⁸ [i]