MinT - Best Known (79, 114, s)-Nets in Base 8

Best Known (79, 114, s)-Nets in Base 8

(79, 114, 402)-Net over F₈ — Constructive and digital

Digital (79, 114, 402)-net over F₈, using

1 times m-reduction [i] based on digital (79, 115, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 29, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]
  2. 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]

(79, 114, 576)-Net in Base 8 — Constructive

(79, 114, 576)-net in base 8, using

8 times m-reduction [i] based on (79, 122, 576)-net in base 8, using
- trace code for nets [i] based on (18, 61, 288)-net in base 64, using
  - 2 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
    - base change [i] based on digital (9, 54, 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]

(79, 114, 2079)-Net over F₈ — Digital

Digital (79, 114, 2079)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 114, 1032131)-Net in Base 8 — Upper bound on s

There is no (79, 114, 1032132)-net in base 8, because

1 times m-reduction [i] would yield (79, 113, 1032132)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 119881 043456 600324 505158 317217 999401 137689 939735 547868 302067 573578 712558 964163 311240 312383 926877 716916 > 8¹¹³ [i]