  We analyze the statistical complexity vs. entropy plane-representation of
sampled chaotic attractors as a function of the sampling period {\tau}. It is
shown that if the Bandt and Pompe procedure is used to assign a probability
distribution function (PDF) to the pertinent time series, the statistical
complexity measure (SCM) attains a definite maximum for a specific sampling
period tM. If the usual histogram approach is used instead in order to assign
the PDF to the time series, the SCM remains almost constant at any sampling
period {\tau}. The significance of tM is further investigated by comparing it
with typical times given in the literature for the two main reconstruction
processes: the Takens' one in a delay-time embedding, and the exact
Nyquist-Shannon reconstruction. It is shown that tM is compatible with those
times recommended as adequate delay ones in Takens' reconstruction. The
reported results correspond to three representative chaotic systems having
correlation dimension 2 < D2 < 3. One recent experiment confirms the analysis
presented here.
