  We present results from a simulation of quenched overlap fermions with
L\"uscher-Weisz gauge field action on lattices up to $24^3 48$ and for pion
masses down to $\approx 250$ MeV. Among the quantities we study are the pion,
rho and nucleon masses, the light and strange quark masses, and the pion decay
constant. The renormalization of the scalar and axial vector currents is done
nonperturbatively in the $RI-MOM$ scheme. The simulations are performed at two
different lattice spacings, $a \approx 0.1$ fm and $\approx 0.15$ fm, and on
two different physical volumes, to test the scaling properties of our action
and to study finite volume effects. We compare our results with the predictions
of chiral perturbation theory and compute several of its low-energy constants.
The pion mass is computed in sectors of fixed topology as well.
