MinT - Best Known (54, 54+22, s)-Nets in Base 3

Best Known (54, 54+22, s)-Nets in Base 3

(54, 54+22, 156)-Net over F₃ — Constructive and digital

Digital (54, 76, 156)-net over F₃, using

3¹ times duplication [i] based on digital (53, 75, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 25, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(54, 54+22, 240)-Net over F₃ — Digital

Digital (54, 76, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+22, 4847)-Net in Base 3 — Upper bound on s

There is no (54, 76, 4848)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 826792 256687 860559 212107 254236 142017 > 3⁷⁶ [i]