MinT - Best Known (225−56, 225, s)-Nets in Base 4

Best Known (225−56, 225, s)-Nets in Base 4

(225−56, 225, 1028)-Net over F₄ — Constructive and digital

Digital (169, 225, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (168, 224, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 56, 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]

(225−56, 225, 2093)-Net over F₄ — Digital

Digital (169, 225, 2093)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−56, 225, 259314)-Net in Base 4 — Upper bound on s

There is no (169, 225, 259315)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2907 360342 038041 391893 669893 733369 101260 501927 642301 515483 936632 440894 895881 828187 291851 234464 310260 300700 070808 927664 604945 316274 342280 > 4²²⁵ [i]