MinT - Best Known (85, 139, s)-Nets in Base 8

Best Known (85, 139, s)-Nets in Base 8

(85, 139, 354)-Net over F₈ — Constructive and digital

Digital (85, 139, 354)-net over F₈, using

17 times m-reduction [i] based on digital (85, 156, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 78, 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]

(85, 139, 432)-Net in Base 8 — Constructive

(85, 139, 432)-net in base 8, using

1 times m-reduction [i] based on (85, 140, 432)-net in base 8, using
- trace code for nets [i] based on (15, 70, 216)-net in base 64, using
  - base change [i] based on digital (5, 60, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(85, 139, 692)-Net over F₈ — Digital

Digital (85, 139, 692)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 139, 69573)-Net in Base 8 — Upper bound on s

There is no (85, 139, 69574)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 338511 237712 600601 178322 758929 603701 051971 494059 096300 169759 158397 977038 382858 491117 848854 006168 341545 170540 545959 113717 733584 > 8¹³⁹ [i]