On optimality and construction of two-treatment circular cross-over designs

The purpose of this article is to determine and construct phi-optimal designs over the class of all circular cross-over designs with two treatments when the number of both periods and experimental subjects is even. We are interested in estimating the contrasts of both direct and carry-over effects jointly, and minimizing the variances of the best linear unbiased estimators of contrasts of direct as well as carry-over effects. These results enrich already existing works in the present literature, strengthening this of Magda (1980), and extending these of Kunert (1984) and Chasiotis and Kounias (2020).