  We show for the first time that collectively jammed disordered packings of
three-dimensional monodisperse frictionless hard spheres can be produced and
tuned using a novel numerical protocol with packing density $\phi$ as low as
0.6. This is well below the value of 0.64 associated with the maximally random
jammed state and entirely unrelated to the ill-defined ``random loose packing''
state density. Specifically, collectively jammed packings are generated with a
very narrow distribution centered at any density $\phi$ over a wide density
range $\phi \in [0.6,~0.74048\ldots]$ with variable disorder. Our results
support the view that there is no universal jamming point that is
distinguishable based on the packing density and frequency of occurence. Our
jammed packings are mapped onto a density-order-metric plane, which provides a
broader characterization of packings than density alone. Other packing
characteristics, such as the pair correlation function, average contact number
and fraction of rattlers are quantified and discussed.
