MinT - Best Known (54−18, 54, s)-Nets in Base 3

Best Known (54−18, 54, s)-Nets in Base 3

(54−18, 54, 84)-Net over F₃ — Constructive and digital

Digital (36, 54, 84)-net over F₃, using

trace code for nets [i] based on digital (0, 18, 28)-net over F₂₇, using
- net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
    - the rational function field F₂₇(x) [i]
  - Niederreiter sequence [i]

(54−18, 54, 118)-Net over F₃ — Digital

Digital (36, 54, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−18, 54, 1503)-Net in Base 3 — Upper bound on s

There is no (36, 54, 1504)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 58 440468 875151 152973 056449 > 3⁵⁴ [i]