MinT - Best Known (27, 27+20, s)-Nets in Base 3

Best Known (27, 27+20, s)-Nets in Base 3

(27, 27+20, 56)-Net over F₃ — Constructive and digital

Digital (27, 47, 56)-net over F₃, using

1 times m-reduction [i] based on digital (27, 48, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 24, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]

(27, 27+20, 386)-Net in Base 3 — Upper bound on s

There is no (27, 47, 387)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 27035 504852 212563 425877 > 3⁴⁷ [i]