  The Cucchieri-Mendes bounds for the gluon propagator are discussed for the
four dimensional pure gauge SU(3) theory. Assuming a pure power law dependence
on the inverse of the lattice volume, the lattice data gives a vanishing zero
momentum gluon propagator in the infinite volume limit. Our investigation shows
that this result is robust against variations of the lattice volumes and
corrections to the power law. Moreover, it is consistent with the
Gribov-Zwanziger horizon condition and contradicts the SU(2) analysis, which
assumed the same type of dependence on the inverse of the volume. Our analysis
considers also more general ansatze that, although not conclusive, open the
possibility of having $D(0) \ne 0$ in the infinite volume limit. A solution to
this puzzle requires further investigations.
