  We investigate the nucleation of superconductivity in a uniform perpendicular
magnetic field H in aluminum microsquares containing a few (2 and 4) submicron
holes (antidots). The normal/superconducting phase boundary T_c(H) of these
structures shows a quite different behavior in low and high fields. In the low
magnetic field regime fluxoid quantization around each antidot leads to
oscillations in T_c(H), expected from the specific sample geometry, and
reminiscent of the network behavior. In high magnetic fields, the T_c(H)
boundaries of the perforated and a reference non-perforated microsquare reveal
cusps at the same values of Phi/Phi_0 (where Phi is the applied flux threading
the total square area and Phi_0 is the superconducting flux quantum), while the
background on T_c(H) becomes quasi-linear, indicating that a giant vortex state
is established. The influence of the actual geometries on T_c(H) is analyzed in
the framework of the linearized Ginzburg-Landau theory.
