MinT - Best Known (86, 86+65, s)-Nets in Base 8

Best Known (86, 86+65, s)-Nets in Base 8

(86, 86+65, 354)-Net over F₈ — Constructive and digital

Digital (86, 151, 354)-net over F₈, using

7 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+65, 460)-Net over F₈ — Digital

Digital (86, 151, 460)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+65, 31241)-Net in Base 8 — Upper bound on s

There is no (86, 151, 31242)-net in base 8, because

1 times m-reduction [i] would yield (86, 150, 31242)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2907 580914 699772 462137 462606 872148 854415 105067 189405 593898 850863 729726 639842 811354 691409 064218 512738 872360 611238 186504 948916 589275 644784 > 8¹⁵⁰ [i]