MinT - Best Known (26−13, 26, s)-Nets in Base 9

Best Known (26−13, 26, s)-Nets in Base 9

(26−13, 26, 164)-Net over F₉ — Constructive and digital

Digital (13, 26, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 13, 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]

(26−13, 26, 3537)-Net in Base 9 — Upper bound on s

There is no (13, 26, 3538)-net in base 9, because

1 times m-reduction [i] would yield (13, 25, 3538)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 718035 984557 354529 132705 > 9²⁵ [i]