MinT - Best Known (93, 93+67, s)-Nets in Base 8

Best Known (93, 93+67, s)-Nets in Base 8

(93, 93+67, 354)-Net over F₈ — Constructive and digital

Digital (93, 160, 354)-net over F₈, using

12 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]

(93, 93+67, 546)-Net over F₈ — Digital

Digital (93, 160, 546)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+67, 42198)-Net in Base 8 — Upper bound on s

There is no (93, 160, 42199)-net in base 8, because

1 times m-reduction [i] would yield (93, 159, 42199)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390438 958145 701834 083910 218198 144288 044904 674923 243891 162933 597636 557734 367244 441786 810584 805699 787484 422593 891026 077477 131215 125294 433084 908140 > 8¹⁵⁹ [i]