MinT - Best Known (120−38, 120, s)-Nets in Base 8

Best Known (120−38, 120, s)-Nets in Base 8

(120−38, 120, 402)-Net over F₈ — Constructive and digital

Digital (82, 120, 402)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (11, 30, 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 (52, 90, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 45, 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]

(120−38, 120, 576)-Net in Base 8 — Constructive

(82, 120, 576)-net in base 8, using

t-expansion [i] based on (81, 120, 576)-net in base 8, using
- 6 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
  - trace code for nets [i] based on (18, 63, 288)-net in base 64, using
    - base change [i] based on digital (9, 54, 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]

(120−38, 120, 1796)-Net over F₈ — Digital

Digital (82, 120, 1796)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−38, 120, 572578)-Net in Base 8 — Upper bound on s

There is no (82, 120, 572579)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 348604 306114 287728 677348 173109 383036 743375 547504 327925 524428 664351 203141 795918 385295 757579 608318 687058 247856 > 8¹²⁰ [i]