Consider an experimental situation where it is desired to compare more than one test treatments with a control treatment. In this paper a method is presented for achieving E-optimal incomplete block design for this situation under the assumption that the observations within each block are correlated. Then an algorithm is provided for making optimal design based on above-mentioned method. This algorithm for any correlation structure with negative non-diagonal elements is applicable.

Neighbour effects, that is the response on a given plot is affected by the treatments in neighbouring plot and the effect by the treatment applied to that plot. As a result, the estimate of treatment differences may deviate because of this interference from neighbouring plots. Neighbour-balanced designs ensure that the treatment comparisons will be as little affected by neighbour effects as possible. Circular neighbour-balanced design are divided into two groups. In the previouse researchs, method of cyclic shifts to construct CNB1 has been used, the authors used this method to construct CNB2. Some series of CNB2 are found by omputer programming using in MATLAB software and method of cyclic shifts. Then, some of these designs witch are universally optimal under models with one sided neighbour effect (M1) are identified.