A Complete Class of Type 1 Optimal Block Designs with Unequal Replications

Abstract

For block designs comparing v treatments in b incomplete blocks of size k, consider settings where bk = vr + 1 and $$r(k-1)=\lambda (v-1)$$ for integers r and $$\lambda $$ . These settings admit designs that possess the symmetry of balanced incomplete block designs and which, though nonbinary, are candidates for optimality in some standard senses. For k = 3, earlier authors have established a class of one binary and one nonbinary design that is complete with respect to all type 1 optimality criteria. Here a solution for the complete class problem for type 1 optimality is obtained for k = 5. The complete class includes two binary and two nonbinary designs.