MinT - Best Known (156−65, 156, s)-Nets in Base 8

Best Known (156−65, 156, s)-Nets in Base 8

(156−65, 156, 354)-Net over F₈ — Constructive and digital

Digital (91, 156, 354)-net over F₈, using

12 times m-reduction [i] based on digital (91, 168, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 84, 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]

(156−65, 156, 547)-Net over F₈ — Digital

Digital (91, 156, 547)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−65, 156, 43243)-Net in Base 8 — Upper bound on s

There is no (91, 156, 43244)-net in base 8, because

1 times m-reduction [i] would yield (91, 155, 43244)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 288611 349375 876113 316417 780852 062190 755867 588153 419026 656509 557082 836417 244044 908708 403571 072878 891344 905486 209824 643398 575041 109370 626863 > 8¹⁵⁵ [i]