MinT - Best Known (119−51, 119, s)-Nets in Base 8

Best Known (119−51, 119, s)-Nets in Base 8

(119−51, 119, 354)-Net over F₈ — Constructive and digital

Digital (68, 119, 354)-net over F₈, using

3 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]

(119−51, 119, 384)-Net over F₈ — Digital

Digital (68, 119, 384)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−51, 119, 26598)-Net in Base 8 — Upper bound on s

There is no (68, 119, 26599)-net in base 8, because

1 times m-reduction [i] would yield (68, 118, 26599)-net in base 8, but
- 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]