Computer-Generated Minimal (and Larger) Response-Surface Designs: (I) The Sphere

Computer-generated designs in the sphere are described which have the minimal (or larger) number of runs for a full quadratic response-surface design. In the case of 3 factors, the designs have 10 through 33 runs; for 4 factors, 15 through 28 runs; for 5 factors, 21 through 33 runs; etc. Some of these designs are listed here in full; the others can be obtained from the authors. The designs were constructed by minimizing the average prediction variance. No prior constraints — such as a central composite structure – are imposed on the locations of the points. The program itself determines the optimal number of runs to make at the center. The best designs found have repeated runs at the center and the remaining runs at points well spread out over the surface of the sphere. There is a simple lower bound on the average prediction variance; this bound is attained by many of the designs.