MinT - Best Known (54, 54+37, s)-Nets in Base 3

Best Known (54, 54+37, s)-Nets in Base 3

(54, 54+37, 80)-Net over F₃ — Constructive and digital

Digital (54, 91, 80)-net over F₃, using

1 times m-reduction [i] based on digital (54, 92, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 46, 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]

(54, 54+37, 93)-Net over F₃ — Digital

Digital (54, 91, 93)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+37, 900)-Net in Base 3 — Upper bound on s

There is no (54, 91, 901)-net in base 3, because

1 times m-reduction [i] would yield (54, 90, 901)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 839906 447595 970486 975466 702221 739624 926609 > 3⁹⁰ [i]