MinT - Best Known (214−48, 214, s)-Nets in Base 3

Best Known (214−48, 214, s)-Nets in Base 3

(214−48, 214, 640)-Net over F₃ — Constructive and digital

Digital (166, 214, 640)-net over F₃, using

3² times duplication [i] based on digital (164, 212, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 53, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(214−48, 214, 1389)-Net over F₃ — Digital

Digital (166, 214, 1389)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−48, 214, 88013)-Net in Base 3 — Upper bound on s

There is no (166, 214, 88014)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 270687 474047 224749 564662 694459 299408 090104 491867 780529 350775 249781 958395 917170 501556 765902 867768 419057 > 3²¹⁴ [i]