MinT - Best Known (65−26, 65, s)-Nets in Base 3

Best Known (65−26, 65, s)-Nets in Base 3

(65−26, 65, 68)-Net over F₃ — Constructive and digital

Digital (39, 65, 68)-net over F₃, using

1 times m-reduction [i] based on digital (39, 66, 68)-net over F₃, using
- trace code for nets [i] based on digital (6, 33, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(65−26, 65, 77)-Net over F₃ — Digital

Digital (39, 65, 77)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−26, 65, 676)-Net in Base 3 — Upper bound on s

There is no (39, 65, 677)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 454045 881666 192658 241544 007739 > 3⁶⁵ [i]