Universal optimality for selected crossover designs

Hedayat and Yang earlier proved that balanced uniform designs in the entire class of crossover designs based on t treatments, n subjects, and p = t periods are universally optimal when n less than or equal to t (t - 1)/2. Surprisingly, in the class of crossover designs with t treatments and p = t periods, a balanced uniform design may not be universally optimal if the number of subjects exceeds t (t -1)/2. This article, among other results, shows that (a) a balanced uniform design is universally optimal in the entire class of' crossover designs with p = t as long as n is not greater than t(t + 2)/2 and 3 less than or equal to t less than or equal to 12; (b) a balanced uniform design with n = 2t, t greater than or equal to 3, and p = t is universally optimal in the entire class of crossover designs with n = 2t and p = t; and (c) for the case where p less than or equal to t, the design suggested by Stufken is universally optimal, thus completing Kushner's result that a Stufken design is universally optimal if n is divisible by t (p - 1).