MinT - Best Known (219−64, 219, s)-Nets in Base 4

Best Known (219−64, 219, s)-Nets in Base 4

(219−64, 219, 531)-Net over F₄ — Constructive and digital

Digital (155, 219, 531)-net over F₄, using

3 times m-reduction [i] based on digital (155, 222, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 74, 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]

(219−64, 219, 1000)-Net over F₄ — Digital

Digital (155, 219, 1000)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−64, 219, 56221)-Net in Base 4 — Upper bound on s

There is no (155, 219, 56222)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 709863 989158 334048 314925 128122 154507 610535 393454 987950 960752 342410 575926 998211 093641 643684 200956 430175 479773 244247 104440 914852 235580 > 4²¹⁹ [i]