MinT - Best Known (209−40, 209, s)-Nets in Base 4

Best Known (209−40, 209, s)-Nets in Base 4

(209−40, 209, 1539)-Net over F₄ — Constructive and digital

Digital (169, 209, 1539)-net over F₄, using

t-expansion [i] based on digital (168, 209, 1539)-net over F₄, using
- 1 times m-reduction [i] based on digital (168, 210, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 70, 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]

(209−40, 209, 8663)-Net over F₄ — Digital

Digital (169, 209, 8663)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−40, 209, 5416398)-Net in Base 4 — Upper bound on s

There is no (169, 209, 5416399)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 676923 182362 112593 193259 541733 130195 145411 813736 084892 682550 394408 948874 537486 728049 894969 591466 519039 510910 712179 048371 683036 > 4²⁰⁹ [i]