A method of constructing optimal sliced uniform designs under discrete discrepancy

Abstract

Sliced uniform designs are useful for generating experimental data with batch structures. In this paper, we employ the discrete discrepancy as the measure of uniformity to construct sliced uniform designs. The construction method is based on an important class of combinatorial configurations, namely, resolvable balanced incomplete block designs; hence, the construction method does not require any computer search. Through resolvable balanced incomplete block designs, under the discrete discrepancy, several infinite classes of new sliced uniform designs are obtained. The obtained design is optimal in the sense that not only the design as a whole but also each of its slices attain the lower bound of the discrete discrepancy. The design parameters are explicitly given, from which experimenters may choose an optimal sliced uniform design with the most suitable run size for their experiment.