Construction of uniform designs via super-simple resolvable t-designs

Abstract

A uniform design seeks design points that are uniformly scattered on the experimental domain. It has been popular since 1980. In this paper, we employ the discrete discrepancy as the measure of uniformity for constructing uniform designs. The equivalency among the discrete discrepancy, non-orthogonal measure E(f_NOD) and minimum generalized aberration (MGA) for comparing U-type designs U(n; q^m) is given. The link between the two apparently unrelated areas of uniform designs and super-simple resolvable t-designs in combinatorial design theory is shown. Through super-simple resolvable t-designs, under the discrete discrepancy, a new method is proposed for constructing uniform designs U_n(q^m), in which any of the q² level-combinations between any two distinct columns can appear at most twice and any two columns are not fully aliased. Many new uniform designs are obtained.