MinT - Best Known (40, 40+39, s)-Nets in Base 9

Best Known (40, 40+39, s)-Nets in Base 9

(40, 40+39, 164)-Net over F₉ — Constructive and digital

Digital (40, 79, 164)-net over F₉, using

1 times m-reduction [i] based on digital (40, 80, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 40, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(40, 40+39, 173)-Net over F₉ — Digital

Digital (40, 79, 173)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+39, 8183)-Net in Base 9 — Upper bound on s

There is no (40, 79, 8184)-net in base 9, because

1 times m-reduction [i] would yield (40, 78, 8184)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 270 033794 005751 468818 455444 286660 611099 592698 783933 866103 880605 450667 374657 > 9⁷⁸ [i]