MinT - Best Known (85, 85+63, s)-Nets in Base 8

Best Known (85, 85+63, s)-Nets in Base 8

(85, 85+63, 354)-Net over F₈ — Constructive and digital

Digital (85, 148, 354)-net over F₈, using

8 times m-reduction [i] based on digital (85, 156, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 78, 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]

(85, 85+63, 475)-Net over F₈ — Digital

Digital (85, 148, 475)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+63, 33968)-Net in Base 8 — Upper bound on s

There is no (85, 148, 33969)-net in base 8, because

1 times m-reduction [i] would yield (85, 147, 33969)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 679103 455324 023599 138588 087642 892297 267099 398069 610636 007998 679385 484356 248203 075069 605489 789909 825109 872428 588338 316103 591796 465184 > 8¹⁴⁷ [i]