  A spatial distribution is hyperuniform if it has local density fluctuations
that vanish in the limit of long length scales. Hyperuniformity is a well known
property of both crystals and quasicrystals. Of recent interest, however, is
disordered hyperuniformity: the presence of hyperuniform scaling without
long-range configurational order. Jammed granular packings have been proposed
as an example of disordered hyperuniformity, but recent numerical investigation
has revealed that many jammed systems instead exhibit a complex set of distinct
behaviors at long, emergent length scales. We use the Voronoi tesselation as a
tool to define a set of rescaling transformations that can impose
hyperuniformity on an arbitrary weighted point process, and show that these
transformations can be used in simulations to iteratively generate
hyperuniform, mechanically stable packings of athermal soft spheres. These
hyperuniform jammed packings display atypical mechanical properties,
particularly in the low-frequency phononic excitations, which exhibit an
isolated band of highly collective modes and a band-gap around zero frequency.
