MinT - Best Known (92−35, 92, s)-Nets in Base 8

Best Known (92−35, 92, s)-Nets in Base 8

(92−35, 92, 354)-Net over F₈ — Constructive and digital

Digital (57, 92, 354)-net over F₈, using

8 times m-reduction [i] based on digital (57, 100, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 50, 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]

(92−35, 92, 384)-Net in Base 8 — Constructive

(57, 92, 384)-net in base 8, using

2 times m-reduction [i] based on (57, 94, 384)-net in base 8, using
- trace code for nets [i] based on (10, 47, 192)-net in base 64, using
  - 2 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
    - base change [i] based on digital (3, 42, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(92−35, 92, 554)-Net over F₈ — Digital

Digital (57, 92, 554)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−35, 92, 69979)-Net in Base 8 — Upper bound on s

There is no (57, 92, 69980)-net in base 8, because

1 times m-reduction [i] would yield (57, 91, 69980)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 15179 421189 005040 104405 041346 534351 940119 322632 236179 635764 651478 550065 799612 197287 > 8⁹¹ [i]