MinT - Best Known (86−43, 86, s)-Nets in Base 9

Best Known (86−43, 86, s)-Nets in Base 9

(86−43, 86, 164)-Net over F₉ — Constructive and digital

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]

(86−43, 86, 175)-Net over F₉ — Digital

Digital (43, 86, 175)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−43, 86, 7890)-Net in Base 9 — Upper bound on s

There is no (43, 86, 7891)-net in base 9, because

1 times m-reduction [i] would yield (43, 85, 7891)-net in base 9, but
- 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]