Generation of space-filling uniform designs in unit hypercubes

In this paper a new discrepancy measure of uniformity for uniform designs (UDs) in a unit cube is presented. Alternative measures of uniformity based on distance criteria which can be applied to higher dimensions are also discussed. The good lattice point (glp) method was used to construct the uniform designs. Two approaches (generator equivalence and projection) of reducing the computational cost of the glp method are proposed and discussed. Two examples are presented in this paper.