Some E-optimal row−column designs having unequally replicated treatments

Abstract We consider the determination and construction of E-optimal row-column designs for usage in experimental situations where heterogeneity is to be eliminated in two directions. In particular, some sufficient conditions are derived for a row-column design to be E-optimal in an experimental setting where υ treatments are to be tested on experimental units arranged in b columns and k rows and where bk/υ is not an integer. Methods for constructing row-column designs satisfying the sufficient conditions for E-optimality obtained are also illustrated.