Universally Optimal One-sided Circular Neighbour-balanced Designs with k = 5

In many experiments, especially in agriculture and horticulture to some extent, the response from a plot in a block is affected by treatments on forward (backward) neighbour plots in the same block. Under such circumstances, one-sided circular neighbour-balanced design (one-sided CNBD) has wide applications. However, in concern with the universal optimality, there are very limited number of known series of one-sided CNBD’s. The purpose of this article is to present a new series of universally optimal one-sided CNBD with block size 5 where if a treatment appears repeatedly in a block, all of them are in a series of adjacent plots in the block.