  We computationally study jammed disordered hard-sphere packings as large as a
million particles. We show that the packings are saturated and hyperuniform,
i.e., that local density fluctuations grow only as a logarithmically-augmented
surface area rather than the volume of the window. The structure factor shows
an unusual non-analytic linear dependence near the origin, $S(k)\sim|k|$. In
addition to exponentially damped oscillations seen in liquids, this implies a
weak power-law tail in the total correlation function, $h(r)\sim-r^{-4}$, and a
long-ranged direct correlation function.
