MinT - Best Known (121−56, 121, s)-Nets in Base 3

Best Known (121−56, 121, s)-Nets in Base 3

(121−56, 121, 60)-Net over F₃ — Constructive and digital

Digital (65, 121, 60)-net over F₃, using

1 times m-reduction [i] based on digital (65, 122, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 61, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(121−56, 121, 82)-Net over F₃ — Digital

Digital (65, 121, 82)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−56, 121, 624)-Net in Base 3 — Upper bound on s

There is no (65, 121, 625)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5547 812503 015042 027537 468842 972950 836916 115308 348697 690801 > 3¹²¹ [i]