MinT - Best Known (83−33, 83, s)-Nets in Base 8

Best Known (83−33, 83, s)-Nets in Base 8

(83−33, 83, 354)-Net over F₈ — Constructive and digital

Digital (50, 83, 354)-net over F₈, using

3 times m-reduction [i] based on digital (50, 86, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 43, 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]

(83−33, 83, 418)-Net over F₈ — Digital

Digital (50, 83, 418)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−33, 83, 41273)-Net in Base 8 — Upper bound on s

There is no (50, 83, 41274)-net in base 8, because

1 times m-reduction [i] would yield (50, 82, 41274)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 113 089208 829126 868044 845299 601972 893460 183786 241777 440534 672350 309007 214249 > 8⁸² [i]