On Construction of Mappable Nearly Orthogonal Arrays with Column-Orthogonality

For designs of computer experiments, two important and desirable properties are projection uniformity and column-orthogonality. However, it is always a challenging task to construct designs with both properties. This paper constructs a series of designs which possess both (near) column-orthogonality and projection uniformity, called (nearly) column-orthogonal mappable nearly orthogonal arrays (MNOAs). Furthermore, we enhance the MNOAs' projection uniformity on any one dimension by using the constructed (nearly) column-orthogonal MNOAs and rotation matrices. Compared with the existing results (such as Sun and Tang in J Am Stat Assoc 112:683-689, 2017), the newly constructed designs are able to accommodate more design columns and have a much better projection uniformity, for the same run sizes.