MinT - Best Known (251−71, 251, s)-Nets in Base 4

Best Known (251−71, 251, s)-Nets in Base 4

(251−71, 251, 531)-Net over F₄ — Constructive and digital

Digital (180, 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]

(251−71, 251, 1292)-Net over F₄ — Digital

Digital (180, 251, 1292)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−71, 251, 92562)-Net in Base 4 — Upper bound on s

There is no (180, 251, 92563)-net in base 4, because

1 times m-reduction [i] would yield (180, 250, 92563)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 273612 435368 347347 131483 065426 219904 802145 210713 391620 667951 510722 935795 003792 833942 564933 506778 217947 943864 548990 303934 457179 285480 576865 447231 980560 > 4²⁵⁰ [i]