MinT - Best Known (199−54, 199, s)-Nets in Base 4

Best Known (199−54, 199, s)-Nets in Base 4

(199−54, 199, 531)-Net over F₄ — Constructive and digital

Digital (145, 199, 531)-net over F₄, using

8 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 69, 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]

(199−54, 199, 1277)-Net over F₄ — Digital

Digital (145, 199, 1277)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−54, 199, 99676)-Net in Base 4 — Upper bound on s

There is no (145, 199, 99677)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 645568 792800 710104 476894 299388 179534 587421 710584 316757 405271 223816 653618 239801 313019 181884 800833 907532 016913 571715 724700 > 4¹⁹⁹ [i]