MinT - Best Known (85, 85+67, s)-Nets in Base 8

Best Known (85, 85+67, s)-Nets in Base 8

(85, 85+67, 354)-Net over F₈ — Constructive and digital

Digital (85, 152, 354)-net over F₈, using

4 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+67, 418)-Net over F₈ — Digital

Digital (85, 152, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 76, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(85, 85+67, 25481)-Net in Base 8 — Upper bound on s

There is no (85, 152, 25482)-net in base 8, because

1 times m-reduction [i] would yield (85, 151, 25482)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23275 451493 747446 936060 024177 778574 338917 618620 380749 755479 266068 329371 518314 557488 882080 607024 952167 084190 957621 344579 101993 300656 083500 > 8¹⁵¹ [i]