Optimal two treatment circular repeated measurements designs up to four periods

We focus on circular repeated measurements designs with t = 2 treatments, n experimental units, and p = 2, 3, 4 periods. Our aim is to obtain phi-optimal designs, for the estimation of contrasts of direct and residual effects jointly, over the class of all designs. Moreover, we are interested in finding designs that minimize the variances of the best linear unbiased estimators of contrasts of direct as well as residual effects over the class of all designs. These results strengthen the work of Magda (1980), and partially the work of Chalikias and Kounias (2017).