MinT - Best Known (59, 100, s)-Nets in Base 8

Best Known (59, 100, s)-Nets in Base 8

(59, 100, 354)-Net over F₈ — Constructive and digital

Digital (59, 100, 354)-net over F₈, using

4 times m-reduction [i] based on digital (59, 104, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 52, 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]

(59, 100, 418)-Net over F₈ — Digital

Digital (59, 100, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 50, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(59, 100, 35022)-Net in Base 8 — Upper bound on s

There is no (59, 100, 35023)-net in base 8, because

1 times m-reduction [i] would yield (59, 99, 35023)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 254663 571460 976159 722684 167955 005318 931645 084151 505696 740784 413572 030230 699281 632117 057996 > 8⁹⁹ [i]