MinT - Best Known (184−62, 184, s)-Nets in Base 3

Best Known (184−62, 184, s)-Nets in Base 3

(184−62, 184, 156)-Net over F₃ — Constructive and digital

Digital (122, 184, 156)-net over F₃, using

16 times m-reduction [i] based on digital (122, 200, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 100, 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]

(184−62, 184, 287)-Net over F₃ — Digital

Digital (122, 184, 287)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−62, 184, 4186)-Net in Base 3 — Upper bound on s

There is no (122, 184, 4187)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6213 307890 687093 378943 663416 725046 161116 438577 491122 142504 315419 915882 375655 108470 495795 > 3¹⁸⁴ [i]