MinT - Best Known (174−47, 174, s)-Nets in Base 4

Best Known (174−47, 174, s)-Nets in Base 4

(174−47, 174, 531)-Net over F₄ — Constructive and digital

Digital (127, 174, 531)-net over F₄, using

6 times m-reduction [i] based on digital (127, 180, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 60, 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]

(174−47, 174, 1159)-Net over F₄ — Digital

Digital (127, 174, 1159)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−47, 174, 106119)-Net in Base 4 — Upper bound on s

There is no (127, 174, 106120)-net in base 4, because

1 times m-reduction [i] would yield (127, 173, 106120)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 346715 575324 044843 782359 592558 904059 353712 850900 482685 466713 790185 761874 473121 162092 524617 286115 217224 > 4¹⁷³ [i]