  In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy
hyperuniform systems can be regarded as hard spheres in Fourier-space in the
sense that the the structure factor is exactly zero in a spherical region
around the origin in analogy with the pair-correlation function of real-space
hard spheres. In this work, we exploit this correspondence to confirm that the
densest Fourier-space hard-sphere system is that of a Bravais lattice. This is
in contrast to real-space hard-spheres, whose densest configuration is
conjectured to be disordered. We also extend the virial series previously
suggested for disordered stealthy hyperuniform systems to higher dimensions in
order to predict spatial decorrelation as function of dimension. This
prediction is then borne out by numerical simulations of disordered stealthy
hyperuniform ground states in dimensions $d=2$-$8$.
