  We experimentally investigate the magnetic field $B$ dependence of the
critical current I_c and the transition temperature T_c, i.e. the I_c(B)-T_c(B)
phase boundary, of superconducting niobium thin films patterned with periodic
and quasiperiodic antidot arrays on the submicron scale. For this purpose we
monitor current-voltage characteristics at different values of B and T. We
investigate samples with antidots positioned at the vertices of two different
tilings with quasiperiodic symmetry, namely the Shield Tiling and the Tuebingen
Triangle Tiling. For reference we investigate a sample with a triangular
antidot lattice. We find modulations of the phase boundary for both
quasiperiodic tilings, which were predicted by numerical simulations but not
observed in experiments yet. The particularity of these commensurability
effects is that they correspond to excess flux densities, which are slightly
higher than the matching flux. The observed matching effects can be explained
by quasiperiodic caging of interstitial vortices and/or the formation of
symmetry induced giant vortices.
