Abstract
Traditional foldover designs are obtained by changing the signs of some columns of an initial design. Li and Lin (Technometrics 58:508–512, 2016) proposed to further improve foldover designs by allowing column permutations. To deal with computational challenges in obtaining the optimal foldover with column permutations, we explore some theoretical properties of such designs. Using the indicator function approach, we investigate under what circumstances can a foldover design be improved by doing column permutations. Several types of permutations are found to be particularly effective for this purpose.
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