MinT - Best Known (61−20, 61, s)-Nets in Base 3

Best Known (61−20, 61, s)-Nets in Base 3

(61−20, 61, 84)-Net over F₃ — Constructive and digital

Digital (41, 61, 84)-net over F₃, using

3¹ times duplication [i] based on digital (40, 60, 84)-net over F₃, using
- trace code for nets [i] based on digital (0, 20, 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]

(61−20, 61, 134)-Net over F₃ — Digital

Digital (41, 61, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(61−20, 61, 1832)-Net in Base 3 — Upper bound on s

There is no (41, 61, 1833)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 127222 392811 016905 194956 787001 > 3⁶¹ [i]