A note on cyclic orthogonal designs

Orthogonality is considered to be one of the most important features for de sign of experiment. in this paper, we investigate orthogonal main-effect de signs with cyclic structure in order to ensure the balance among all design columns. We show that such designs exist for a any number of factors (L) a nd moreover, they are not unique. An explicit form for D-efficiency of cycl ic orthogonal designs is derived. It is shown that D-optimal cyclic design essentially involves minimizing the tightness of the experimental range. Th e minimum tightness D-optimal cyclic orthogonal designs are presented and t abulated for k < 10.