On the construction of nested orthogonal arrays with the adjacent numbers of levels

Nested orthogonal arrays (NOAs) provide an option for designing an experimental setup consisting of two experiments, with the expensive higher‐precision experiment nested within a larger and relatively inexpensive lower‐precision experiment. Construction of NOAs with the adjacent numbers of levels is a challenging problem. In this paper, we present several methods for constructing such NOAs and obtain some classes of such new symmetric NOAs in which the larger arrays have minimum run size. These methods are also extended to construction of NOAs with more than two layers. Furthermore, by adding some columns to these symmetric NOAs, we can construct a lot of new asymmetric NOAs. Illustrative examples are given.