MinT - Best Known (140−54, 140, s)-Nets in Base 8

Best Known (140−54, 140, s)-Nets in Base 8

(140−54, 140, 354)-Net over F₈ — Constructive and digital

Digital (86, 140, 354)-net over F₈, using

18 times m-reduction [i] based on digital (86, 158, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 79, 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]

(140−54, 140, 432)-Net in Base 8 — Constructive

(86, 140, 432)-net in base 8, using

t-expansion [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]

(140−54, 140, 721)-Net over F₈ — Digital

Digital (86, 140, 721)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−54, 140, 75145)-Net in Base 8 — Upper bound on s

There is no (86, 140, 75146)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 708648 681386 699407 139444 370241 543958 663646 054545 242483 045992 908986 885858 145355 823947 074599 063677 100922 086447 046268 615483 522752 > 8¹⁴⁰ [i]