MinT - Best Known (86, 86+59, s)-Nets in Base 8

Best Known (86, 86+59, s)-Nets in Base 8

(86, 86+59, 354)-Net over F₈ — Constructive and digital

Digital (86, 145, 354)-net over F₈, using

13 times m-reduction [i] based on 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+59, 574)-Net over F₈ — Digital

Digital (86, 145, 574)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+59, 50836)-Net in Base 8 — Upper bound on s

There is no (86, 145, 50837)-net in base 8, because

1 times m-reduction [i] would yield (86, 144, 50837)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11092 139611 551957 450058 880404 016472 317062 235241 037932 492504 494526 926931 856542 185455 033405 589243 994645 302781 942266 933525 559713 326848 > 8¹⁴⁴ [i]