MinT - Best Known (57−27, 57, s)-Nets in Base 9

Best Known (57−27, 57, s)-Nets in Base 9

(57−27, 57, 200)-Net over F₉ — Constructive and digital

Digital (30, 57, 200)-net over F₉, using

1 times m-reduction [i] based on digital (30, 58, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 29, 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]

(57−27, 57, 9131)-Net in Base 9 — Upper bound on s

There is no (30, 57, 9132)-net in base 9, because

1 times m-reduction [i] would yield (30, 56, 9132)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 274130 400530 292651 531467 401177 924773 987373 758483 187425 > 9⁵⁶ [i]