MinT - Best Known (105−45, 105, s)-Nets in Base 8

Best Known (105−45, 105, s)-Nets in Base 8

(105−45, 105, 354)-Net over F₈ — Constructive and digital

Digital (60, 105, 354)-net over F₈, using

1 times m-reduction [i] based on digital (60, 106, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 53, 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]

(105−45, 105, 24024)-Net in Base 8 — Upper bound on s

There is no (60, 105, 24025)-net in base 8, because

1 times m-reduction [i] would yield (60, 104, 24025)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8344 650000 156519 077601 026681 400342 612871 510067 926619 453450 479610 700987 688201 165285 494766 229316 > 8¹⁰⁴ [i]