Box, Michael J.; Draper, Norman R. (1974, ASQC and the American Statistical Association) University of Wisconsin, Madison, WI
In this note, we discuss k-factor, second order designs with minimum number of points 1/2(k + 1)(k + 2), in particular, those which are extensions of designs that give minimum generalized variance for k = 2 and 3. The experimental region is the unit cuboid. Minimum point designs of this type are unknown for K > or = 4, and these designs are the best found to date except for k = 4, where a better design is known. Kiefer has shown that these designs cannot be the best for k > o r= 7, via an existence result but, even here, specific better designs are not known and appear difficult to obtain. We also discuss some difficulties of using, in practice, designs that are D-optimal (that is give minimum generalized variance when the number of points is not restricted).