MinT - Best Known (225−67, 225, s)-Nets in Base 4

Best Known (225−67, 225, s)-Nets in Base 4

(225−67, 225, 531)-Net over F₄ — Constructive and digital

Digital (158, 225, 531)-net over F₄, using

t-expansion [i] based on digital (157, 225, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 75, 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]

(225−67, 225, 946)-Net over F₄ — Digital

Digital (158, 225, 946)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−67, 225, 53545)-Net in Base 4 — Upper bound on s

There is no (158, 225, 53546)-net in base 4, because

1 times m-reduction [i] would yield (158, 224, 53546)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 726 994669 334906 099787 706560 928770 426260 483660 853932 997338 328863 098040 993492 404150 191267 452913 425258 505932 127840 764698 369125 601828 770043 > 4²²⁴ [i]