SOME OPTIMAL DESIGNS OF BLOCK SIZE 2

Cheng and Constantine (J. Statistical Planning and Inference, 15, 1986) showed the E-optimality of some regular graph designs when the block size k greater-than-or-equal-to 3. For k=2, they could only prove the E-optimality over equireplicate designs. In this paper. we remove the restriction to equireplicate designs, thereby establishing the E-optimality of many designs with k=2 over the whole class of competing designs. As an application, we establish the E-optimality of a class of partially balanced incomplete block designs with a rectangular association scheme. Finally a simple method for constructing highly efficient designs of block size two is discussed.