In the last years, there has been substantial progress in the rigorous justification of the Lee-Huang-Yang prediction for the ground state energy density of dilute Bose gases. While lower bounds have been derived for very general repulsive interactions, so far the upper bound has only been proven for square integrable potentials. In this talk, I am going to present a new upper bound for the ground state energy, completing the derivation of the Lee-Huang-Yang formula for dilute hard spheres. This is a joint work with G. Basti, M. Brooks, S. Cenatiempo and A. Olgiati.