MinT - Best Known (68, 68+50, s)-Nets in Base 8

Best Known (68, 68+50, s)-Nets in Base 8

(68, 68+50, 354)-Net over F₈ — Constructive and digital

Digital (68, 118, 354)-net over F₈, using

4 times m-reduction [i] based on digital (68, 122, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 61, 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]

(68, 68+50, 418)-Net over F₈ — Digital

Digital (68, 118, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 59, 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]

(68, 68+50, 26598)-Net in Base 8 — Upper bound on s

There is no (68, 118, 26599)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36710 567800 620048 921018 096801 450925 308504 410764 483754 228730 924028 822086 159789 810566 567032 017207 390643 177624 > 8¹¹⁸ [i]