MinT - Best Known (221−61, 221, s)-Nets in Base 4

Best Known (221−61, 221, s)-Nets in Base 4

(221−61, 221, 531)-Net over F₄ — Constructive and digital

Digital (160, 221, 531)-net over F₄, using

t-expansion [i] based on digital (159, 221, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (159, 228, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 76, 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]

(221−61, 221, 1294)-Net over F₄ — Digital

Digital (160, 221, 1294)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−61, 221, 104393)-Net in Base 4 — Upper bound on s

There is no (160, 221, 104394)-net in base 4, because

1 times m-reduction [i] would yield (160, 220, 104394)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 839885 274276 615212 220141 261109 091648 763921 849685 640466 604611 019487 344800 628356 024085 513631 477239 449191 162140 653642 394446 357402 894752 > 4²²⁰ [i]