MinT - Best Known (86, 86+69, s)-Nets in Base 8

Best Known (86, 86+69, s)-Nets in Base 8

(86, 86+69, 354)-Net over F₈ — Constructive and digital

Digital (86, 155, 354)-net over F₈, using

3 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+69, 407)-Net over F₈ — Digital

Digital (86, 155, 407)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+69, 23793)-Net in Base 8 — Upper bound on s

There is no (86, 155, 23794)-net in base 8, because

1 times m-reduction [i] would yield (86, 154, 23794)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 920829 510236 055761 627236 561406 936015 758254 470425 097847 816622 330515 300799 097085 121157 661097 096070 148611 236131 993616 639664 576122 815458 867640 > 8¹⁵⁴ [i]