MinT - Best Known (132−56, 132, s)-Nets in Base 3

Best Known (132−56, 132, s)-Nets in Base 3

(132−56, 132, 80)-Net over F₃ — Constructive and digital

Digital (76, 132, 80)-net over F₃, using

4 times m-reduction [i] based on digital (76, 136, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 68, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(132−56, 132, 111)-Net over F₃ — Digital

Digital (76, 132, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−56, 132, 975)-Net in Base 3 — Upper bound on s

There is no (76, 132, 976)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 962 551791 041095 955365 719881 914897 969370 364846 904030 281253 149057 > 3¹³² [i]