MinT - Best Known (209−52, 209, s)-Nets in Base 4

Best Known (209−52, 209, s)-Nets in Base 4

(209−52, 209, 1028)-Net over F₄ — Constructive and digital

Digital (157, 209, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (156, 208, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 52, 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]

(209−52, 209, 1966)-Net over F₄ — Digital

Digital (157, 209, 1966)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−52, 209, 243091)-Net in Base 4 — Upper bound on s

There is no (157, 209, 243092)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 676946 036245 423796 283825 359508 871489 298435 898415 701668 650905 660859 227250 387342 514861 623178 163864 791467 567962 381133 781969 547856 > 4²⁰⁹ [i]