MinT - Best Known (55, 55+35, s)-Nets in Base 8

Best Known (55, 55+35, s)-Nets in Base 8

(55, 55+35, 354)-Net over F₈ — Constructive and digital

Digital (55, 90, 354)-net over F₈, using

6 times m-reduction [i] based on digital (55, 96, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 48, 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]

(55, 55+35, 384)-Net in Base 8 — Constructive

(55, 90, 384)-net in base 8, using

trace code for nets [i] based on (10, 45, 192)-net in base 64, using
- 4 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
  - base change [i] based on digital (3, 42, 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]

(55, 55+35, 492)-Net over F₈ — Digital

Digital (55, 90, 492)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+35, 54790)-Net in Base 8 — Upper bound on s

There is no (55, 90, 54791)-net in base 8, because

1 times m-reduction [i] would yield (55, 89, 54791)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 237 170155 867027 134653 518307 698932 901422 473586 698757 584391 968348 607640 696670 056000 > 8⁸⁹ [i]