MinT - Best Known (105, 105+68, s)-Nets in Base 8

Best Known (105, 105+68, s)-Nets in Base 8

(105, 105+68, 354)-Net over F₈ — Constructive and digital

Digital (105, 173, 354)-net over F₈, using

8¹ times duplication [i] based on digital (104, 172, 354)-net over F₈, using
- t-expansion [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(105, 105+68, 432)-Net in Base 8 — Constructive

(105, 173, 432)-net in base 8, using

8¹ times duplication [i] based on (104, 172, 432)-net in base 8, using
- trace code for nets [i] based on (18, 86, 216)-net in base 64, using
  - 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
    - base change [i] based on digital (5, 78, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(105, 105+68, 784)-Net over F₈ — Digital

Digital (105, 173, 784)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+68, 76100)-Net in Base 8 — Upper bound on s

There is no (105, 173, 76101)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 716264 212916 513527 391081 318802 529899 594454 430464 453329 056882 902102 775150 168909 071440 964920 823894 798879 381875 961867 769662 201823 111688 206675 590873 468549 685108 > 8¹⁷³ [i]