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The purpose of this article is to determine and construct-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).

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