MinT - Best Known (171−71, 171, s)-Nets in Base 8

Best Known (171−71, 171, s)-Nets in Base 8

(171−71, 171, 354)-Net over F₈ — Constructive and digital

Digital (100, 171, 354)-net over F₈, using

t-expansion [i] based on digital (93, 171, 354)-net over F₈, using
- 1 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]

(171−71, 171, 601)-Net over F₈ — Digital

Digital (100, 171, 601)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−71, 171, 48350)-Net in Base 8 — Upper bound on s

There is no (100, 171, 48351)-net in base 8, because

1 times m-reduction [i] would yield (100, 170, 48351)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3351 996615 782380 103907 732998 809855 883129 542609 213200 305003 713992 505688 761236 866655 319011 162502 828846 834311 621608 974711 665384 919647 769837 267350 855678 855784 > 8¹⁷⁰ [i]