MinT - Best Known (143−47, 143, s)-Nets in Base 8

Best Known (143−47, 143, s)-Nets in Base 8

(143−47, 143, 402)-Net over F₈ — Constructive and digital

Digital (96, 143, 402)-net over F₈, using

8¹ times duplication [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]

(143−47, 143, 576)-Net in Base 8 — Constructive

(96, 143, 576)-net in base 8, using

9 times m-reduction [i] based on (96, 152, 576)-net in base 8, using
- trace code for nets [i] based on (20, 76, 288)-net in base 64, using
  - 1 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]

(143−47, 143, 1673)-Net over F₈ — Digital

Digital (96, 143, 1673)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−47, 143, 506926)-Net in Base 8 — Upper bound on s

There is no (96, 143, 506927)-net in base 8, because

1 times m-reduction [i] would yield (96, 142, 506927)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 295272 200128 181734 296270 416808 851901 013865 098908 021311 792588 350415 183733 343059 128501 566212 051799 177208 069771 651491 968145 978976 > 8¹⁴² [i]