MinT - Best Known (209, 209+50, s)-Nets in Base 4

Best Known (209, 209+50, s)-Nets in Base 4

(209, 209+50, 1544)-Net over F₄ — Constructive and digital

Digital (209, 259, 1544)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (0, 25, 5)-net over F₄, using
  - net from sequence [i] based on digital (0, 4)-sequence over F₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 0 and N(F) ≥ 5, using
      - the rational function field F₄(x) [i]
    - Niederreiter sequence [i]
2. digital (184, 234, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 78, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(209, 209+50, 9718)-Net over F₄ — Digital

Digital (209, 259, 9718)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209, 209+50, 5859284)-Net in Base 4 — Upper bound on s

There is no (209, 259, 5859285)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 858102 051606 210266 580817 097925 327946 499297 490934 013834 226944 406880 708228 475256 320299 016080 351880 574902 117937 881077 975677 438807 145907 733644 950675 937682 980032 > 4²⁵⁹ [i]