MinT - Best Known (86−36, 86, s)-Nets in Base 8

Best Known (86−36, 86, s)-Nets in Base 8

(86−36, 86, 354)-Net over F₈ — Constructive and digital

Digital (50, 86, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 43, 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]

(86−36, 86, 22262)-Net in Base 8 — Upper bound on s

There is no (50, 86, 22263)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 463250 651647 995357 469084 124407 285833 028607 438114 376226 161625 176146 103064 857641 > 8⁸⁶ [i]