MinT - Best Known (170−68, 170, s)-Nets in Base 8

Best Known (170−68, 170, s)-Nets in Base 8

(170−68, 170, 354)-Net over F₈ — Constructive and digital

Digital (102, 170, 354)-net over F₈, using

t-expansion [i] based on digital (93, 170, 354)-net over F₈, using
- 2 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]

(170−68, 170, 384)-Net in Base 8 — Constructive

(102, 170, 384)-net in base 8, using

2 times m-reduction [i] based on (102, 172, 384)-net in base 8, using
- trace code for nets [i] based on (16, 86, 192)-net in base 64, using
  - 5 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
    - base change [i] based on digital (3, 78, 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]

(170−68, 170, 711)-Net over F₈ — Digital

Digital (102, 170, 711)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−68, 170, 63340)-Net in Base 8 — Upper bound on s

There is no (102, 170, 63341)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3352 998005 254388 181467 438428 538762 461813 551900 192973 521536 499042 177771 829789 620484 985723 581527 439286 417742 843920 716608 053649 798288 252555 827100 014779 821606 > 8¹⁷⁰ [i]