A class of optimal row-column designs with some empty cells

Agrawal (1966) constructed a series of row column designs with row-column incidence structure J - I. We show that there exist designs which strongly dominate Agrawal's designs for all v greater than or equal to 4 and are therefore to be preferred with respect to any optimality criterion. These dominating designs are E-optimal within the entire class of such row-column designs and are also highly A- and D-efficient. Some methods for constructing such designs are also developed.