MinT - Best Known (214−80, 214, s)-Nets in Base 3

Best Known (214−80, 214, s)-Nets in Base 3

(214−80, 214, 156)-Net over F₃ — Constructive and digital

Digital (134, 214, 156)-net over F₃, using

10 times m-reduction [i] based on digital (134, 224, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 112, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(214−80, 214, 241)-Net over F₃ — Digital

Digital (134, 214, 241)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−80, 214, 2774)-Net in Base 3 — Upper bound on s

There is no (134, 214, 2775)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 271121 521435 627475 234983 995686 174898 891922 197316 156898 885972 696417 592002 150827 282584 439564 730772 580913 > 3²¹⁴ [i]