MinT - Best Known (186−70, 186, s)-Nets in Base 3

Best Known (186−70, 186, s)-Nets in Base 3

(186−70, 186, 156)-Net over F₃ — Constructive and digital

Digital (116, 186, 156)-net over F₃, using

2 times m-reduction [i] based on digital (116, 188, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 94, 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]

(186−70, 186, 209)-Net over F₃ — Digital

Digital (116, 186, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−70, 186, 2352)-Net in Base 3 — Upper bound on s

There is no (116, 186, 2353)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56042 843367 580104 038868 121095 432276 938354 275000 823270 795100 576688 757873 620537 592448 952539 > 3¹⁸⁶ [i]