Reduction of the number of pairs in paired comparison designs and exact designs for quadratic models

The construction of designs in paired comparisons experiments is considered. In Berkum (1987) D-optimal designs are given under the assumption of no treatment differences. These designs can not be used in most practical applications since they entail different weights. Also, the number of pairs is (too) large. In this paper D-optimal designs are given with a reduced number of pairs (approximate theory) and exact designs are given with a high efficiency. This is done for a quadratic model for 2, 3, 4 and 5 dimensions and a hypercube as experimental region