D-optimum and quasi-D-optimum second-order designs on a cube

Abstract

The D -optimum designs and their sets of support are studied for quadratic regression on a cube. The structure of such designs is found and the designs presented have either the least possible, or considerably fewer, points of support than Kôno's D -optimum designs and the designs of Farrell, Kiefer & Walbran (1967). The sets of support of the D -optimum designs are used for the construction of integer designs, the characteristics of which are tabulated.