MinT - Best Known (75, 107, s)-Nets in Base 8

Best Known (75, 107, s)-Nets in Base 8

(75, 107, 402)-Net over F₈ — Constructive and digital

Digital (75, 107, 402)-net over F₈, using

t-expansion [i] based on digital (74, 107, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 27, 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 (47, 80, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 40, 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]

(75, 107, 576)-Net in Base 8 — Constructive

(75, 107, 576)-net in base 8, using

t-expansion [i] based on (73, 107, 576)-net in base 8, using
- 5 times m-reduction [i] based on (73, 112, 576)-net in base 8, using
  - trace code for nets [i] based on (17, 56, 288)-net in base 64, using
    - base change [i] based on digital (9, 48, 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]

(75, 107, 2338)-Net over F₈ — Digital

Digital (75, 107, 2338)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 107, 1063777)-Net in Base 8 — Upper bound on s

There is no (75, 107, 1063778)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 271978 302058 237470 652293 089934 087266 032536 853274 217383 218060 216054 089624 662835 434505 176427 468914 > 8¹⁰⁷ [i]