MinT - Best Known (174−49, 174, s)-Nets in Base 4

Best Known (174−49, 174, s)-Nets in Base 4

(174−49, 174, 531)-Net over F₄ — Constructive and digital

Digital (125, 174, 531)-net over F₄, using

3 times m-reduction [i] based on digital (125, 177, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 59, 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]

(174−49, 174, 973)-Net over F₄ — Digital

Digital (125, 174, 973)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−49, 174, 71445)-Net in Base 4 — Upper bound on s

There is no (125, 174, 71446)-net in base 4, because

1 times m-reduction [i] would yield (125, 173, 71446)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 389919 544367 619515 870011 471128 143947 375916 318033 118276 525961 568213 066206 193674 322673 621851 058638 160416 > 4¹⁷³ [i]