MinT - Best Known (96, 157, s)-Nets in Base 8

Best Known (96, 157, s)-Nets in Base 8

(96, 157, 354)-Net over F₈ — Constructive and digital

Digital (96, 157, 354)-net over F₈, using

t-expansion [i] based on digital (93, 157, 354)-net over F₈, using
- 15 times m-reduction [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]

(96, 157, 432)-Net in Base 8 — Constructive

(96, 157, 432)-net in base 8, using

1 times m-reduction [i] based on (96, 158, 432)-net in base 8, using
- trace code for nets [i] based on (17, 79, 216)-net in base 64, using
  - 5 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
    - base change [i] based on digital (5, 72, 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]

(96, 157, 765)-Net over F₈ — Digital

Digital (96, 157, 765)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 157, 85440)-Net in Base 8 — Upper bound on s

There is no (96, 157, 85441)-net in base 8, because

1 times m-reduction [i] would yield (96, 156, 85441)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 315793 330903 387477 688424 495027 489064 727018 233556 938290 781040 758028 723381 875561 377808 152631 870151 381382 550319 112211 014028 150080 063981 445728 > 8¹⁵⁶ [i]