Measures of uniformity for space-filling uniform designs in a spherical region. (2016) - Talke, Ismael S.; Borkowski, John J.
The focus of this paper is to present and discuss new discrepancy measures of uniform designs (UDs) in the two- and three-dimensional spherical design regions B 2 and B 3 . The good lattice point (glp) method is used to construct the UDs in B 2 and B 3 because it generates good space-filling designs with low discrepancy and designs having small distance-based measures of uniformity. The best UDs were found in B 2 and B 3 for newly proposed discrepancy criteria. Best UDs based on three distance-based assessment criteria are also included for comparison. Distance-based criteria are alternative measures for design generation in higher-dimensional spherical regions with an example of design generation presented for B 4 .