MinT - Best Known (130−50, 130, s)-Nets in Base 8

Best Known (130−50, 130, s)-Nets in Base 8

(130−50, 130, 354)-Net over F₈ — Constructive and digital

Digital (80, 130, 354)-net over F₈, using

16 times m-reduction [i] based on digital (80, 146, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 73, 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]

(130−50, 130, 432)-Net in Base 8 — Constructive

(80, 130, 432)-net in base 8, using

trace code for nets [i] based on (15, 65, 216)-net in base 64, using
- 5 times m-reduction [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]

(130−50, 130, 690)-Net over F₈ — Digital

Digital (80, 130, 690)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−50, 130, 72194)-Net in Base 8 — Upper bound on s

There is no (80, 130, 72195)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2522 462443 850053 374967 107282 952001 138566 416602 590902 042756 248368 131349 208889 529753 139638 917024 731837 482372 691276 285312 > 8¹³⁰ [i]