Universal optimality of balanced uniform crossover des

Kunert [Ann. Statist. 12 (1984) 1006-1017] proved that, in the class of repeated measurement designs based on t treatments, p=t periods and n=(lambda t) experimental units, a balanced uniform design is universally optimal for direct treatment effects if t >= 3 and (lambda)=1, or if t >=6 and (lambda)=2. This result is generalized to t>=3 as long as (lambda)<= (t-1)/2.