MinT - Best Known (69, 69+52, s)-Nets in Base 3

Best Known (69, 69+52, s)-Nets in Base 3

(69, 69+52, 80)-Net over F₃ — Constructive and digital

Digital (69, 121, 80)-net over F₃, using

1 times m-reduction [i] based on digital (69, 122, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 61, 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]

(69, 69+52, 100)-Net over F₃ — Digital

Digital (69, 121, 100)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+52, 851)-Net in Base 3 — Upper bound on s

There is no (69, 121, 852)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5516 461970 002229 577460 548828 675441 942255 366642 225257 521305 > 3¹²¹ [i]