  We study the critical behavior of the 3-state Potts model, where the spins
are located at the centers of the occupied squares of the deterministic
Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo
simulations, for a Hausdorff dimension $d_{f}$ $\simeq 1.8928$. The phase
transition is shown to be a second order one. The maxima of the susceptibility
of the order parameter follow a power law in a very reliable way, which enables
us to calculate the ratio of the exponents $\gamma /\nu$. We find that the
scaling corrections affect the behavior of most of the thermodynamical
quantities. However, the sequence of intersection points extracted from the
Binder's cumulant provides bounds for the critical temperature. We are able to
give the bounds for the exponent $1/\nu$ as well as for the ratio of the
exponents $\beta/\nu$, which are compatible with the results calculated from
the hyperscaling relation.
