A note on the bounds of efficiency factor and ER optimality of block designs

Das and Kageyama (1991) obtained upper bounds of efficiency factor of a connected block design with v treatments and b blocks of size k each and considered a class of E optimal proper efficiency balanced designs (strictly saying Das and Kageyama considered ER-optimality of some class of block designs). In this paper we extend this theory on block designs with unequal block sizes and we consider ER optimality of some class of connected nonbinary block designs with unequal block sizes.