MinT - Best Known (189−54, 189, s)-Nets in Base 4

Best Known (189−54, 189, s)-Nets in Base 4

(189−54, 189, 531)-Net over F₄ — Constructive and digital

Digital (135, 189, 531)-net over F₄, using

3 times m-reduction [i] based on digital (135, 192, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 64, 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]

(189−54, 189, 975)-Net over F₄ — Digital

Digital (135, 189, 975)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−54, 189, 59641)-Net in Base 4 — Upper bound on s

There is no (135, 189, 59642)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 615920 068993 381727 373460 952619 395076 886243 843032 854539 024732 082672 438443 953628 652825 652135 353539 837286 445302 487520 > 4¹⁸⁹ [i]