MinT - Best Known (55−18, 55, s)-Nets in Base 3

Best Known (55−18, 55, s)-Nets in Base 3

(55−18, 55, 84)-Net over F₃ — Constructive and digital

Digital (37, 55, 84)-net over F₃, using

3¹ times duplication [i] based on 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]

(55−18, 55, 127)-Net over F₃ — Digital

Digital (37, 55, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−18, 55, 1699)-Net in Base 3 — Upper bound on s

There is no (37, 55, 1700)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 174 985175 002170 402957 892681 > 3⁵⁵ [i]