MinT - Best Known (86, 86+72, s)-Nets in Base 8

Best Known (86, 86+72, s)-Nets in Base 8

(86, 86+72, 354)-Net over F₈ — Constructive and digital

Digital (86, 158, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 79, 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]

(86, 86+72, 376)-Net over F₈ — Digital

Digital (86, 158, 376)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+72, 18735)-Net in Base 8 — Upper bound on s

There is no (86, 158, 18736)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48779 603741 803723 162318 746956 197433 496817 739447 755179 563370 461467 513132 757649 296345 486094 944750 029821 643002 060495 961427 180550 308700 084796 697801 > 8¹⁵⁸ [i]