MinT - Best Known (86, 86+67, s)-Nets in Base 8

Best Known (86, 86+67, s)-Nets in Base 8

(86, 86+67, 354)-Net over F₈ — Constructive and digital

Digital (86, 153, 354)-net over F₈, using

5 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+67, 432)-Net over F₈ — Digital

Digital (86, 153, 432)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+67, 27140)-Net in Base 8 — Upper bound on s

There is no (86, 153, 27141)-net in base 8, because

1 times m-reduction [i] would yield (86, 152, 27141)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186266 135996 942943 961409 363212 201033 499995 773059 094613 305867 009456 676246 486917 414303 167808 075172 278346 591783 122388 672423 766324 880947 065024 > 8¹⁵² [i]