Optimal designs for comparisons between two sets of treatments (Q1082757)

The paper gives methods for the construction of optimal block designs for v treatments which are divided into two sets containing u and \(w=v-u\) treatments. The optimal designs are obtained for estimating all differences of two treatments, one from each set. It is proved that D(u,w,b,k) contains an A-optimal design. Problems of constructing optimal designs for small and large block sizes k have been dealt with separately. Optimal row-column designs for v treatments arranged in an array are also considered. The set of optimal designs derived in this paper can have a lot of applications in agricultural and biological experiments.