MinT - Best Known (65−21, 65, s)-Nets in Base 3

Best Known (65−21, 65, s)-Nets in Base 3

(65−21, 65, 84)-Net over F₃ — Constructive and digital

Digital (44, 65, 84)-net over F₃, using

1 times m-reduction [i] based on digital (44, 66, 84)-net over F₃, using
- trace code for nets [i] based on digital (0, 22, 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]

(65−21, 65, 146)-Net over F₃ — Digital

Digital (44, 65, 146)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−21, 65, 2552)-Net in Base 3 — Upper bound on s

There is no (44, 65, 2553)-net in base 3, because

1 times m-reduction [i] would yield (44, 64, 2553)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 444694 093794 993219 895609 129049 > 3⁶⁴ [i]