MinT - Best Known (65, 65+35, s)-Nets in Base 8

Best Known (65, 65+35, s)-Nets in Base 8

(65, 65+35, 354)-Net over F₈ — Constructive and digital

Digital (65, 100, 354)-net over F₈, using

16 times m-reduction [i] based on digital (65, 116, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 58, 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]

(65, 65+35, 518)-Net in Base 8 — Constructive

(65, 100, 518)-net in base 8, using

base change [i] based on digital (40, 75, 518)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (40, 76, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 38, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(65, 65+35, 893)-Net over F₈ — Digital

Digital (65, 100, 893)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+35, 186206)-Net in Base 8 — Upper bound on s

There is no (65, 100, 186207)-net in base 8, because

1 times m-reduction [i] would yield (65, 99, 186207)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 254650 004262 709508 585053 403446 677866 883701 986976 262877 484622 265303 014351 470965 228361 673126 > 8⁹⁹ [i]