MinT - Best Known (27−12, 27, s)-Nets in Base 3

Best Known (27−12, 27, s)-Nets in Base 3

(27−12, 27, 32)-Net over F₃ — Constructive and digital

Digital (15, 27, 32)-net over F₃, using

1 times m-reduction [i] based on digital (15, 28, 32)-net over F₃, using
- trace code for nets [i] based on digital (1, 14, 16)-net over F₉, using
  - net from sequence [i] based on digital (1, 15)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
      - a function field by GarcÃa and Quoos [i]

(27−12, 27, 34)-Net over F₃ — Digital

Digital (15, 27, 34)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(27−12, 27, 204)-Net in Base 3 — Upper bound on s

There is no (15, 27, 205)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 720059 731473 > 3²⁷ [i]