Construction of Some Families of Asymmetric Column‐Orthogonal Designs

Latin hypercube designs have been widely used for computer experiments, but they are constrained by the requirement that the number of levels for each factor must be equal to the run size. To address this limitation, previous studies have relaxed this restriction and provided methods to construct column‐orthogonal designs. Subsequent work has further extended these efforts by developing new approaches for constructing asymmetric column‐orthogonal designs (ACODs). However, these existing methods are still limited by the number of levels or the number of factors. The aim of the present paper is to construct some families of ACODs with a more flexible number of factors or levels. Some of the resulting designs ensure that the estimates of main effects of all factors are not only uncorrelated with each other but also uncorrelated with the estimates of all quadratic effects and bilinear interactions.