MinT - Best Known (77, 77+57, s)-Nets in Base 8

Best Known (77, 77+57, s)-Nets in Base 8

(77, 77+57, 354)-Net over F₈ — Constructive and digital

Digital (77, 134, 354)-net over F₈, using

6 times m-reduction [i] based on digital (77, 140, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 70, 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]

(77, 77+57, 450)-Net over F₈ — Digital

Digital (77, 134, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 67, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(77, 77+57, 31429)-Net in Base 8 — Upper bound on s

There is no (77, 134, 31430)-net in base 8, because

1 times m-reduction [i] would yield (77, 133, 31430)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 291262 862445 140013 621418 466039 157319 122459 699747 159258 074947 002649 365552 833261 728220 895883 409136 461568 590221 705371 533672 > 8¹³³ [i]