MinT - Best Known (250−62, 250, s)-Nets in Base 4

Best Known (250−62, 250, s)-Nets in Base 4

(250−62, 250, 1028)-Net over F₄ — Constructive and digital

Digital (188, 250, 1028)-net over F₄, using

4² times duplication [i] based on digital (186, 248, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 62, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(250−62, 250, 2335)-Net over F₄ — Digital

Digital (188, 250, 2335)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−62, 250, 296617)-Net in Base 4 — Upper bound on s

There is no (188, 250, 296618)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 273478 252927 104983 397265 949138 878616 256053 864077 646317 398806 654302 488816 429187 322289 679374 458289 231276 006503 464725 781850 590750 607233 272693 101054 188720 > 4²⁵⁰ [i]