MinT - Best Known (60, 60+27, s)-Nets in Base 8

Best Known (60, 60+27, s)-Nets in Base 8

(60, 60+27, 382)-Net over F₈ — Constructive and digital

Digital (60, 87, 382)-net over F₈, using

8¹ times duplication [i] based on digital (59, 86, 382)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 18, 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 (41, 68, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 34, 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]

(60, 60+27, 576)-Net in Base 8 — Constructive

(60, 87, 576)-net in base 8, using

1 times m-reduction [i] based on (60, 88, 576)-net in base 8, using
- trace code for nets [i] based on (16, 44, 288)-net in base 64, using
  - 5 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
    - base change [i] based on digital (9, 42, 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]

(60, 60+27, 1598)-Net over F₈ — Digital

Digital (60, 87, 1598)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+27, 763117)-Net in Base 8 — Upper bound on s

There is no (60, 87, 763118)-net in base 8, because

1 times m-reduction [i] would yield (60, 86, 763118)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 463174 244462 328285 048610 864417 291299 189619 270022 552171 593426 598331 298158 494307 > 8⁸⁶ [i]