MinT - Best Known (134−40, 134, s)-Nets in Base 8

Best Known (134−40, 134, s)-Nets in Base 8

(134−40, 134, 484)-Net over F₈ — Constructive and digital

Digital (94, 134, 484)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (20, 40, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 20, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
2. digital (54, 94, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 47, 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]

(134−40, 134, 576)-Net in Base 8 — Constructive

(94, 134, 576)-net in base 8, using

14 times m-reduction [i] based on (94, 148, 576)-net in base 8, using
- trace code for nets [i] based on (20, 74, 288)-net in base 64, using
  - 3 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
    - base change [i] based on digital (9, 66, 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]

(134−40, 134, 2807)-Net over F₈ — Digital

Digital (94, 134, 2807)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−40, 134, 1333236)-Net in Base 8 — Upper bound on s

There is no (94, 134, 1333237)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 329132 349439 265187 488395 157969 208491 183798 149613 538716 402130 577774 142655 607047 531727 109163 068851 856722 582733 928178 974939 > 8¹³⁴ [i]