MinT - Best Known (159−64, 159, s)-Nets in Base 8

Best Known (159−64, 159, s)-Nets in Base 8

(159−64, 159, 354)-Net over F₈ — Constructive and digital

Digital (95, 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]

(159−64, 159, 384)-Net in Base 8 — Constructive

(95, 159, 384)-net in base 8, using

1 times m-reduction [i] based on (95, 160, 384)-net in base 8, using
- trace code for nets [i] based on (15, 80, 192)-net in base 64, using
  - 4 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]

(159−64, 159, 652)-Net over F₈ — Digital

Digital (95, 159, 652)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−64, 159, 56086)-Net in Base 8 — Upper bound on s

There is no (95, 159, 56087)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390416 544828 992489 073247 543920 267062 363823 430777 074642 650772 795360 085649 409952 229007 624417 393269 684362 379802 477580 245333 067092 700017 938733 552888 > 8¹⁵⁹ [i]