Abstract: We report optimality aspects of row-column designs for 7 treatments, 7 rows, and 7 columns with three treatment replications within the class of designs with row-column, row-treatment, and column-treatment incidence matrices generated by binary circulants. In particular, we find a 3-way BIBD which doubles the efficiencies of the Agrawal (1966a,b) design for all three factors, and which is optimal w.r.t. Kiefer's Φp-criteria within this class of designs. Also it turns out to be universally optimal within a large subclass of designs.
Key words and phrases: BIBD, 3-way BIBD, circulants, Loewner partial ordering, Φp-optimality, row-column designs, Schur optimality, universal optimality.