MinT - Best Known (59−25, 59, s)-Nets in Base 9

Best Known (59−25, 59, s)-Nets in Base 9

(59−25, 59, 300)-Net over F₉ — Constructive and digital

Digital (34, 59, 300)-net over F₉, using

1 times m-reduction [i] based on digital (34, 60, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 30, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(59−25, 59, 308)-Net over F₉ — Digital

Digital (34, 59, 308)-net over F₉, using

1 times m-reduction [i] based on digital (34, 60, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 30, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(59−25, 59, 27060)-Net in Base 9 — Upper bound on s

There is no (34, 59, 27061)-net in base 9, because

1 times m-reduction [i] would yield (34, 58, 27061)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22 193039 450918 795529 710407 887373 331317 834804 615042 025313 > 9⁵⁸ [i]