On the optimality of block designs

Summary A family of highly efficient designs in the sence of theE-criterion is herein described. These designs have strictly betterE-performance than regular graph designs, yet the off-diagonal entries of theirC-matrix differ by as much as two. Some counterexamples to conjectures in experimental design are then supplied. Asymptotic behavior and equivalence of theA- andD-criteria under a certain condition of uniqueness are analyzed as well.