  We present a N-dimensional quantization a la Berezin-Klauder or frame
quantization of the complex plane based on overcomplete families of states
(coherent states) generated by the N first harmonic oscillator eigenstates. The
spectra of position and momentum operators are finite and eigenvalues are
equal, up to a factor, to the zeros of Hermite polynomials. From numerical and
theoretical studies of the large $N$ behavior of the product $\lambda\_m(N)
\lambda\_M(N)$ of non null smallest positive and largest eigenvalues, we infer
the inequality $\delta\_N(Q) \Delta\_N(Q) = \sigma\_N \overset{<}{\underset{N
\to \infty}{\to}} 2 \pi$ (resp. $\delta\_N(P) \Delta\_N(P) = \sigma\_N
\overset{<}{\underset{N \to \infty}{\to}} 2 \pi $) involving, in suitable
units, the minimal ($\delta\_N(Q)$) and maximal ($\Delta\_N(Q)$) sizes of
regions of space (resp. momentum) which are accessible to exploration within
this finite-dimensional quantum framework. Interesting issues on the
measurement process and connections with the finite Chern-Simons matrix model
for the Quantum Hall effect are discussed.
