MinT - Best Known (66, 66+46, s)-Nets in Base 8

Best Known (66, 66+46, s)-Nets in Base 8

(66, 66+46, 354)-Net over F₈ — Constructive and digital

Digital (66, 112, 354)-net over F₈, using

6 times m-reduction [i] based on digital (66, 118, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 59, 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]

(66, 66+46, 450)-Net over F₈ — Digital

Digital (66, 112, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 56, 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]

(66, 66+46, 33637)-Net in Base 8 — Upper bound on s

There is no (66, 112, 33638)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 139989 346491 283892 745821 933270 534484 210881 720939 168410 601677 346242 364002 532631 924344 585199 449109 839184 > 8¹¹² [i]