MinT - Best Known (150−68, 150, s)-Nets in Base 8

Best Known (150−68, 150, s)-Nets in Base 8

(150−68, 150, 354)-Net over F₈ — Constructive and digital

Digital (82, 150, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 75, 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]

(150−68, 150, 367)-Net over F₈ — Digital

Digital (82, 150, 367)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−68, 150, 18625)-Net in Base 8 — Upper bound on s

There is no (82, 150, 18626)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2911 726925 618825 569926 994713 389987 352519 616705 773301 398013 812481 648649 455282 934951 595487 028117 074321 195373 593146 139200 503899 965951 181824 > 8¹⁵⁰ [i]