Circular neighbor-balanced designs using cyclic shifts

In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and construct circular neighbor-balanced designs (CNBDs) by the method of cyclic shifts or sets of shifts. An important feature of this method is that the properties of a design can be easily obtained from the sets of shifts instead of constructing the actual blocks of the design. That is, the off-diagonal elements of the concurrence matrix can be easily obtained from the sets of shifts. Since the suggested designs are circular, balanced and binary, so they are universally optimal.