On the E-optimality of complete designs under an interference model

In the experiments in which the response to a treatment can be affected by other treatments, the interference model with neighbor effects is usually applied. It is known, that circular neighbor balanced designs (CNBDs) are universally optimal under this model. However, such designs cannot exist for each combination of design parameters. If in the class of block designs with a given number of blocks there exists CNBD, then such a design cannot exist in the class with one block less or more. The aim of this paper is to identify the E-optimal complete block designs under the interference model with neighbor effects over such classes of designs. The results are based on algebraic properties of the information matrix.