MinT - Best Known (56, 56+24, s)-Nets in Base 3

Best Known (56, 56+24, s)-Nets in Base 3

(56, 56+24, 144)-Net over F₃ — Constructive and digital

Digital (56, 80, 144)-net over F₃, using

1 times m-reduction [i] based on digital (56, 81, 144)-net over F₃, using
- trace code for nets [i] based on digital (2, 27, 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]

(56, 56+24, 217)-Net over F₃ — Digital

Digital (56, 80, 217)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+24, 3998)-Net in Base 3 — Upper bound on s

There is no (56, 80, 3999)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 148 042799 495833 826517 891650 812877 273577 > 3⁸⁰ [i]