MinT - Best Known (57, 57+39, s)-Nets in Base 9

Best Known (57, 57+39, s)-Nets in Base 9

(57, 57+39, 344)-Net over F₉ — Constructive and digital

Digital (57, 96, 344)-net over F₉, using

4 times m-reduction [i] based on digital (57, 100, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 50, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(57, 57+39, 497)-Net over F₉ — Digital

Digital (57, 96, 497)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+39, 58513)-Net in Base 9 — Upper bound on s

There is no (57, 96, 58514)-net in base 9, because

1 times m-reduction [i] would yield (57, 95, 58514)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 499403 425833 926153 479466 372559 972314 770402 826237 329529 293134 700869 041053 133458 588524 780785 > 9⁹⁵ [i]