Variance balanced circular designs involving sequences of treatments with first and second residuals

Designs involving sequences of treatments (also called changeover, crossover, or repeated measurements designs) balanced for first and second residuals available in literature are usually large even for a moderate number of treatments. Besides, most of these designs require number of periods at least equal to the number of treatments. In this paper a class of variance balanced circular designs for prime or prime power number of treatments, v ( = m p + 1 ; m, a positive integer) using p ( ⩾ 4 , < v ) periods and only mv experimental units has been proposed. A simple method of analysis of these designs is given and the efficiency factors relative to the orthogonal designs have been tabulated for v ⩽ 31 and p ⩾ 4 , ⩽ 12 .