MinT - Best Known (141−46, 141, s)-Nets in Base 8

Best Known (141−46, 141, s)-Nets in Base 8

(141−46, 141, 402)-Net over F₈ — Constructive and digital

Digital (95, 141, 402)-net over F₈, using

1 times m-reduction [i] based on digital (95, 142, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 34, 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 (61, 108, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 54, 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]

(141−46, 141, 576)-Net in Base 8 — Constructive

(95, 141, 576)-net in base 8, using

9 times m-reduction [i] based on (95, 150, 576)-net in base 8, using
- trace code for nets [i] based on (20, 75, 288)-net in base 64, using
  - 2 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
    - base change [i] based on digital (9, 66, 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]

(141−46, 141, 1724)-Net over F₈ — Digital

Digital (95, 141, 1724)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−46, 141, 463104)-Net in Base 8 — Upper bound on s

There is no (95, 141, 463105)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 661893 870828 656125 518642 621233 756283 909338 972118 018299 411911 186821 949526 958981 226171 521656 640166 205975 148782 588573 875042 462976 > 8¹⁴¹ [i]