We investigate experimentally and theoretically the superconducting properties of an Al thin film covering a periodic array of Co/Pt magnetic disks with out-of-plane magnetization for different radii of the magnetic disks and constant period of the magnetic lattice. The presence of the arrays of magnetic dots leads to a quantized displacement of the normal/superconducting phase boundary along the magnetic field axis, with each step corresponding to a flux-quantum per unit cell of the magnetic lattice. We demonstrate that this so-called field-induced superconductivity is strongly dependent not only on the chosen magnetic material and its magnetization M but also on the radius R of the constructed magnetic disks. Since field-induced superconductivity is directly linked to the nucleation of vortex-antivortex (V-AV) pairs, a theoretical M-R equilibrium phase boundary is presented, delimiting regions of different numbers of induced V-AV pairs per magnet. A good qualitative and quantitative agreement is found between theory and experiment.