A-efficient balanced treatment incomplete block designs

The purpose of this paper is to present a large number of highly A-efficient incomplete block designs for making comparisons among a set of test treatments and a control treatment. These designs are BTIB designs. A simple method of construction of BTIB designs, based on BIB designs is proposed. The advantage of this method is that one can use the vast literature on BIB designs to obtain a large number of highly A-efficient BTIB designs. In several cases, for a given number of test treatments and given block size, these efficient designs require far fewer number of blocks than the corresponding A-optimal designs available in the literature.