MinT - Best Known (55, 55+39, s)-Nets in Base 8

Best Known (55, 55+39, s)-Nets in Base 8

(55, 55+39, 354)-Net over F₈ — Constructive and digital

Digital (55, 94, 354)-net over F₈, using

2 times m-reduction [i] based on digital (55, 96, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 48, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(55, 55+39, 371)-Net over F₈ — Digital

Digital (55, 94, 371)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+39, 29808)-Net in Base 8 — Upper bound on s

There is no (55, 94, 29809)-net in base 8, because

1 times m-reduction [i] would yield (55, 93, 29809)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 971875 276359 839406 780498 693048 688910 209964 560722 190486 905092 534322 825630 978817 625888 > 8⁹³ [i]