MinT - Best Known (193−55, 193, s)-Nets in Base 4

Best Known (193−55, 193, s)-Nets in Base 4

(193−55, 193, 531)-Net over F₄ — Constructive and digital

Digital (138, 193, 531)-net over F₄, using

t-expansion [i] based on digital (137, 193, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (137, 195, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 65, 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]

(193−55, 193, 1003)-Net over F₄ — Digital

Digital (138, 193, 1003)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−55, 193, 69576)-Net in Base 4 — Upper bound on s

There is no (138, 193, 69577)-net in base 4, because

1 times m-reduction [i] would yield (138, 192, 69577)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39 406841 531897 496952 441740 819609 576770 556262 903475 024900 594164 378508 975271 769423 246518 022360 087775 477874 822184 285120 > 4¹⁹² [i]