MinT - Best Known (96, 96+63, s)-Nets in Base 8

Best Known (96, 96+63, s)-Nets in Base 8

(96, 96+63, 354)-Net over F₈ — Constructive and digital

Digital (96, 159, 354)-net over F₈, using

t-expansion [i] based on digital (93, 159, 354)-net over F₈, using
- 13 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, 96+63, 384)-Net in Base 8 — Constructive

(96, 159, 384)-net in base 8, using

3 times m-reduction [i] based on (96, 162, 384)-net in base 8, using
- trace code for nets [i] based on (15, 81, 192)-net in base 64, using
  - 3 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
    - base change [i] based on digital (3, 72, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(96, 96+63, 703)-Net over F₈ — Digital

Digital (96, 159, 703)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+63, 71066)-Net in Base 8 — Upper bound on s

There is no (96, 159, 71067)-net in base 8, because

1 times m-reduction [i] would yield (96, 158, 71067)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48798 303588 378075 991234 834924 921412 325513 525537 866876 571730 554824 629825 382574 831586 290630 016475 633848 889579 802457 904791 717306 657113 244096 440960 > 8¹⁵⁸ [i]