Construction of uniform designs without replications

A uniform design scatters its design points evenly on the experimental domain according to some discrepancy measure. In this paper all the design points of a full factorial design can be split into two subdesigns. One is called the complementary design of the other. The complementary design theories of characterizing one design through the other under the four commonly used discrepancy measures are investigated. Based on these complementary design theories, some general rules for searching uniform designs through their complementary designs are proposed. An efficient method to check if a design has repeated points is introduced and a modified threshold-accepting algorithm is proposed to search uniform or nearly uniform designs without replications. The new algorithm is shown to be more efficient by comparing with other existing methods. Many new uniform or nearly uniform designs without replications are tabulated and compared.