Construction of trend-free optimal block designs under some correlation structures

In many block experiments where the treatments are applied to the experimental units sequentially over time or space, there may be a systematic trend effect that influences the observations in addition to the block and the treatment effects. In some previous literature, optimality of block designs under trend effects has been studied in the case of uncorrelated observations when the number of treatments is greater than the size of blocks. This article deals with the block model incorporating trend components when the observations are correlated under some correlation structures. We introduce methods for constructing trend-free optimal designs with every treatment number and block size.