MinT - Best Known (206−51, 206, s)-Nets in Base 4

Best Known (206−51, 206, s)-Nets in Base 4

(206−51, 206, 1028)-Net over F₄ — Constructive and digital

Digital (155, 206, 1028)-net over F₄, using

4² times duplication [i] based on digital (153, 204, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 51, 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]

(206−51, 206, 1988)-Net over F₄ — Digital

Digital (155, 206, 1988)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−51, 206, 293336)-Net in Base 4 — Upper bound on s

There is no (155, 206, 293337)-net in base 4, because

1 times m-reduction [i] would yield (155, 205, 293337)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 291920 878948 987033 538877 369926 914000 979967 248203 146236 505616 778423 403969 797771 200129 403869 546347 595031 601895 320704 603988 > 4²⁰⁵ [i]