  We demonstrate the existence of large phononic band gaps in designed
hyperuniform (isotropic) disordered two-dimensional (2D) phononic structures of
Pb cylinders in epoxy matrix. The phononic band gaps in hyperuniform disordered
phononic structures are comparable to band gaps of similar periodic structures,
for both out-of-plane and in-plane polarizations. A large number of localized
modes is identified near the band edges, as well as, diffusive transmission
throughout the rest of the frequency spectrum. Very high-Q cavity modes for
both out-of-plane and in-plane polarizations are formed by selectively removing
a single cylinder out of the structure. Efficient waveguiding with almost 100%
transmission trough waveguide structures with arbitrary bends is also
presented. We expand our results to thin three-dimensional layers of such
structures and demonstrate effective band gaps related to the respective 2D
band gaps. Moreover, the drop in the Q factor for the three-dimensional
structures is not more than three orders of magnitude compared to the 2D ones.
