MinT - Best Known (83, 83+42, s)-Nets in Base 8

Best Known (83, 83+42, s)-Nets in Base 8

(83, 83+42, 382)-Net over F₈ — Constructive and digital

Digital (83, 125, 382)-net over F₈, using

1 times m-reduction [i] based on digital (83, 126, 382)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 26, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]
  2. digital (57, 100, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 50, 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]

(83, 83+42, 576)-Net in Base 8 — Constructive

(83, 125, 576)-net in base 8, using

t-expansion [i] based on (81, 125, 576)-net in base 8, using
- 1 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]

(83, 83+42, 1327)-Net over F₈ — Digital

Digital (83, 125, 1327)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+42, 294381)-Net in Base 8 — Upper bound on s

There is no (83, 125, 294382)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 76958 030786 201077 382569 162778 211427 171660 340493 640230 465761 507349 797040 391701 337104 046827 966942 566362 415791 622390 > 8¹²⁵ [i]