Optimal non-circular designs for total effects under interference models

In block designs, the responses of plots are potentially influenced by the treatments of neighbouring plots and the surrounding environment. Many researchers use two guarding plots next to the edge plots, for which we apply certain treatments to control these environmental effects. Thus, a design is presented as a collection of treatment sequences. For the estimation of total effects, existing results consider circular designs, whose constraints are unnecessary in common applications. In this paper, we construct optimal or highly efficient non-circular designs under interference models. It is observed that the optimal non-circular designs for the total effects outperform the optimal circular designs in many instances. In fact, a design containing a circular sequence cannot be optimal for $t>2$.