  Orthogonal array, a classical and effective tool for collecting data, has
been flourished with its applications in modern computer experiments and
engineering statistics. Driven by the wide use of computer experiments with
both qualitative and quantitative factors, multiple computer experiments,
multi-fidelity computer experiments, cross-validation and stochastic
optimization, orthogonal arrays with certain structures have been introduced.
Sliced orthogonal arrays and nested orthogonal arrays are examples of such
arrays. This article introduces a flexible, fresh construction method which
uses smaller arrays and a special structure. The method uncovers the hidden
structure of many existing fixed-level orthogonal arrays of given run sizes,
possibly with more columns. It also allows fixed-level orthogonal arrays of
nearly strength three to be constructed, which are useful as there are not many
construction methods for fixed-level orthogonal arrays of strength three, and
also helpful for generating Latin hypercube designs with desirable
low-dimensional projections. Theoretical properties of the proposed method are
explored. As by-products, several theoretical results on orthogonal arrays are
obtained.
