MinT - Best Known (54, 77, s)-Nets in Base 3

Best Known (54, 77, s)-Nets in Base 3

(54, 77, 144)-Net over F₃ — Constructive and digital

Digital (54, 77, 144)-net over F₃, using

1 times m-reduction [i] based on digital (54, 78, 144)-net over F₃, using
- trace code for nets [i] based on digital (2, 26, 48)-net over F₂₇, using
  - net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]

(54, 77, 215)-Net over F₃ — Digital

Digital (54, 77, 215)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 77, 4847)-Net in Base 3 — Upper bound on s

There is no (54, 77, 4848)-net in base 3, because

1 times m-reduction [i] would yield (54, 76, 4848)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 826792 256687 860559 212107 254236 142017 > 3⁷⁶ [i]