MinT - Best Known (198−55, 198, s)-Nets in Base 4

Best Known (198−55, 198, s)-Nets in Base 4

(198−55, 198, 531)-Net over F₄ — Constructive and digital

Digital (143, 198, 531)-net over F₄, using

6 times m-reduction [i] based on digital (143, 204, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 68, 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]

(198−55, 198, 1148)-Net over F₄ — Digital

Digital (143, 198, 1148)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−55, 198, 89947)-Net in Base 4 — Upper bound on s

There is no (143, 198, 89948)-net in base 4, because

1 times m-reduction [i] would yield (143, 197, 89948)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40357 965943 590333 902022 096142 364553 911880 442092 009576 504319 408148 891960 511074 519194 969955 556527 302626 177714 363616 042795 > 4¹⁹⁷ [i]