MinT - Best Known (162, 250, s)-Nets in Base 3

Best Known (162, 250, s)-Nets in Base 3

(162, 250, 162)-Net over F₃ — Constructive and digital

Digital (162, 250, 162)-net over F₃, using

t-expansion [i] based on digital (157, 250, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(162, 250, 328)-Net over F₃ — Digital

Digital (162, 250, 328)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 250, 4390)-Net in Base 3 — Upper bound on s

There is no (162, 250, 4391)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 191038 958679 636621 922185 935308 396962 106177 822024 659289 781133 125830 308229 043170 381388 351806 778545 298850 864420 348125 114025 > 3²⁵⁰ [i]