MinT - Best Known (40, 40+30, s)-Nets in Base 9

Best Known (40, 40+30, s)-Nets in Base 9

(40, 40+30, 320)-Net over F₉ — Constructive and digital

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+30, 334)-Net over F₉ — Digital

Digital (40, 70, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 35, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(40, 40+30, 22784)-Net in Base 9 — Upper bound on s

There is no (40, 70, 22785)-net in base 9, because

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]