  Quantum black holes within the loop quantum gravity (LQG) framework are
considered. The number of microscopic states that are consistent with a black
hole of a given horizon area $A_0$ are counted and the statistical entropy, as
a function of the area, is obtained for $A_0$ up to $550 l^2_{\rm Pl}$. The
results are consistent with an asymptotic linear relation and a logarithmic
correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that
yields the asymptotic linear relation compatible with the Bekenstein-Hawking
entropy is shown to coincide with a value close to $\gamma=0.274$, which has
been previously obtained analytically. However, a new and oscillatory
functional form for the entropy is found for small, Planck size, black holes
that calls for a physical interpretation.
