The Super Proton Synchrotron (SPS) injection system plays a fundamental role to preserve the quality of injected high-brightness beams for the LHC physics program and to maintain the maximum storable intensity. The present system was not conceived for such intensities and beam qualities, being the result of years of upgrades and patches. In this study, we propose the design of a completely new injection system based on numerical optimisation, including realistic hardware assumptions. We also present a framework to minimise the batch spacing of the LHC beams, as this directly translates in the maximum achievable luminosity in the LHC.