Run orders for efficient two level experimental plans with minimum factor level changes robust to time trends

In this paper we construct run orders of orthogonal arrays with 12≤n≤28$12\le n\le 28$ runs and 4≤q≤6$4\le q\le 6$ factors that minimize the number of level changes of each factor. The corresponding orthogonal arrays can estimate a model with all main effects and their two factor interactions with the highest efficiency and also provide estimates of all main effects that are independent of linear and quadratic time (or position) trends. Some alternative efficient run orders are also presented when the estimation of two factor interactions is of experimental interest.