MinT - Best Known (85−42, 85, s)-Nets in Base 9

Best Known (85−42, 85, s)-Nets in Base 9

(85−42, 85, 164)-Net over F₉ — Constructive and digital

Digital (43, 85, 164)-net over F₉, using

1 times m-reduction [i] based on digital (43, 86, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 43, 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]

(85−42, 85, 182)-Net over F₉ — Digital

Digital (43, 85, 182)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−42, 85, 7890)-Net in Base 9 — Upper bound on s

There is no (43, 85, 7891)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1290 897272 480736 783349 093720 738053 560151 088646 268354 565448 239309 168060 297627 777401 > 9⁸⁵ [i]