MinT - Best Known (38, 38+18, s)-Nets in Base 3

Best Known (38, 38+18, s)-Nets in Base 3

(38, 38+18, 84)-Net over F₃ — Constructive and digital

Digital (38, 56, 84)-net over F₃, using

1 times m-reduction [i] based on digital (38, 57, 84)-net over F₃, using
- trace code for nets [i] based on digital (0, 19, 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]

(38, 38+18, 137)-Net over F₃ — Digital

Digital (38, 56, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+18, 1921)-Net in Base 3 — Upper bound on s

There is no (38, 56, 1922)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 525 416172 460310 074640 652597 > 3⁵⁶ [i]