MinT - Best Known (116−49, 116, s)-Nets in Base 8

Best Known (116−49, 116, s)-Nets in Base 8

(116−49, 116, 354)-Net over F₈ — Constructive and digital

Digital (67, 116, 354)-net over F₈, using

4 times m-reduction [i] based on digital (67, 120, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 60, 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]

(116−49, 116, 418)-Net over F₈ — Digital

Digital (67, 116, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 58, 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]

(116−49, 116, 29740)-Net in Base 8 — Upper bound on s

There is no (67, 116, 29741)-net in base 8, because

1 times m-reduction [i] would yield (67, 115, 29741)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 71 682089 837488 006911 177482 345286 444767 024760 917595 845825 328814 968210 363848 560027 256602 603722 868102 348918 > 8¹¹⁵ [i]