Statistica Sinica 12(2002), 931-939

${E(s^2)}$-OPTIMALITY AND MINIMUM DISCREPANCY IN

2-LEVEL SUPERSATURATED DESIGNS

Min-Qian Liu and Fred J. Hickernell

Tianjin University and Hong Kong Baptist University

Abstract: Supersaturated experimental designs are often assessed by the $E(s^2)$ criterion, and some methods have been found for constructing $E(s^2)$-optimal designs. Another criterion for assessing experimental designs is discrepancy, of which there are several different kinds. The discrepancy measures how much the empirical distribution of the design points deviates from the uniform distribution. Here it is shown that for 2-level supersaturated designs the $E(s^2)$ criterion and a certain discrepancy share the same optimal designs.

Key words and phrases: Hamming distance, reproducing kernel, uniformity.