Latinized, Improved Lhs, and Cvt Point Sets in Hypercubes

Abstract. It is shown how an arbitrary set of points in the hypercube can be Latinized, i.e., can be transformed into a point set that has the Latin hypercube property. The effect of Latinization on the star discrepancy and other uniformity measures of a point set is analyzed. For a few selected but representative point sampling methods, evidence is provided to show that Latinization lowers the star discrepancy measure. A novel point sampling method is presented based on centroidal Voronoi tessellations of the hypercube. These point sets have excellent volumetric distributions, but have poor star discrepancies. Evidence is given that the Latinization of CVT points sets greatly lowers their star discrepancy measure but still preserves superior volumetric uniformity. As a result, means for determining improved Latin hypercube point samples are given.