The CALiPPSO.jl package implements a new algorithm for producing disordered spheres packings with very high accuracy. The algorithm reaches the critical jamming point of hard spheres through a chain of constrained linear optimization problems. CALiPPSO.jl exploits the functionality of JuMP for modelling and is thus compatible with several optimizers. In collaboration with C. Artiaco, G. Parisi, and F. Ricci Tersenghi.