For the class of repeated measurements designs based on $t$ treatments, $n$ experimental units and two periods, the following results are obtained. 1. The equivalence of the information matrices of such repeated measurements designs and of certain block designs is established. The implication of this equivalence on the optimality of both repeated measurements designs and block designs is explored. 2. A family of universally optimal designs or $A$-optimal designs is constructed depending whether or not $n$ divides $t$. 3. Families of optimal designs for residual effects and for comparing test treatments with a control are constructed.
"Optimal Two-Period Repeated Measurements Designs." Ann. Statist. 18 (4) 1805 - 1816, December, 1990. https://doi.org/10.1214/aos/1176347879