MinT - Best Known (25−11, 25, s)-Nets in Base 9

Best Known (25−11, 25, s)-Nets in Base 9

(25−11, 25, 200)-Net over F₉ — Constructive and digital

Digital (14, 25, 200)-net over F₉, using

1 times m-reduction [i] based on digital (14, 26, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 13, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(25−11, 25, 12388)-Net in Base 9 — Upper bound on s

There is no (14, 25, 12389)-net in base 9, because

1 times m-reduction [i] would yield (14, 24, 12389)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 79782 927087 423173 933385 > 9²⁴ [i]