Efficient Augmented Block Designs for Unreplicated Test Treatments Along with Replicated Controls

Augmented block designs for unreplicated test treatments are investigated under the A- and MV-criteria with respect to test versus test, control versus test and control versus control comparisons. We derive design-independent lower bounds on these criteria over a wide class of competing designs. These bounds are useful benchmarks and the resulting expressions for efficiencies enable objective assessment of any given design under theA- and MV-criteria. It is seen that the use of BIB designs and duals thereof as well as existing block design catalogs often leads to very high efficiencies for all three types of comparisons. Illustrative examples, including a large-scale one, are presented.