Optimal row-column design for three treatments

The A-optimality problem is solved for three treatments in a row-column layout. Depending on the numbers of rows and columns, the requirements for optimality can be decidedly counterintuitive: replication numbers need not be as equal as possible, and trace of the information matrix need not be maximal. General rules for comparing 3×3 information matrices for their A-behavior are also developed, and the A-optimality problem is also solved for three treatments in simple block designs.