Circular neighbour-balanced designs and one-sided circular neighbour-balanced designs

In most block designs for agricultural experiments, the nature of the yield underlying treatments may reach such a stage that the treatment received by a plot may influence the response on the neighbouring plots of the same block or sometimes it may influence the response only on the following plot. As an example of the second type, the tall varieties may affect the crops grown on the neighbouring plots by their shades. Bailey (J Indian Soc Agric Stat 56(3):302–314, 2003) has developed a type of design concerned with the study of one sided neighbour effects for application under such conditions. This paper gives, introducing a lemma, constructions of new series of (i) Circular Neighbour-Balanced designs and (ii) One-sided Circular Neighbour-Balanced designs.