MinT - Best Known (95−31, 95, s)-Nets in Base 8

Best Known (95−31, 95, s)-Nets in Base 8

(95−31, 95, 379)-Net over F₈ — Constructive and digital

Digital (64, 95, 379)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 19, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. digital (45, 76, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 38, 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]

(95−31, 95, 576)-Net in Base 8 — Constructive

(64, 95, 576)-net in base 8, using

1 times m-reduction [i] based on (64, 96, 576)-net in base 8, using
- trace code for nets [i] based on (16, 48, 288)-net in base 64, using
  - 1 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
    - base change [i] based on digital (9, 42, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(95−31, 95, 1261)-Net over F₈ — Digital

Digital (64, 95, 1261)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−31, 95, 418815)-Net in Base 8 — Upper bound on s

There is no (64, 95, 418816)-net in base 8, because

1 times m-reduction [i] would yield (64, 94, 418816)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7 770736 231693 856027 619161 649833 347899 706709 585205 236414 480327 856003 611699 529169 282945 > 8⁹⁴ [i]