MinT - Best Known (251−69, 251, s)-Nets in Base 4

Best Known (251−69, 251, s)-Nets in Base 4

(251−69, 251, 531)-Net over F₄ — Constructive and digital

Digital (182, 251, 531)-net over F₄, using

t-expansion [i] based on digital (179, 251, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, 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]

(251−69, 251, 1467)-Net over F₄ — Digital

Digital (182, 251, 1467)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−69, 251, 120549)-Net in Base 4 — Upper bound on s

There is no (182, 251, 120550)-net in base 4, because

1 times m-reduction [i] would yield (182, 250, 120550)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 273798 383094 434719 754340 794688 172080 429089 820225 629080 372140 593086 588811 655368 567143 177752 525259 323841 388594 736381 838311 560873 795779 308791 466610 573702 > 4²⁵⁰ [i]