The efficient sampling of a general multidimensional distribution function presents a long-standing problem in diverse fields of numerical analysis. For non-trivial systems, Monte Carlo methods are the standard approach, producing a set of points in configuration space that sample the desired distribution. However, there are apparent flaws with this approach: namely the inevitable clustering of points in certain regions of configuration space while other sections are left undersampled. We have introduced a new sampling method, Quasi-Regular Grids (QRG), which results in an optimally distributed set of points that maintain local uniformity while simultaneously sampling any desired distribution. These new grids are then applied to the challenging problem of computing the vibrational spectra for both model and molecular systems. By constructing a distributed Gaussian basis using a QRG and solving the vibrational Schrodinger equation we quantitatively demonstrate the superiority of the method compared to existing approaches in the literature.