Abstract: Orthogonal arrays have numerous applications in various areas like design of experiments, survey sampling and cryptology. A special type of orthogonal arrays are the nested orthogonal arrays. These arrays have practical use in the planning of experiments consisting of two experiments, the expensive one of higher accuracy being nested in a larger and relatively inexpensive one of lower accuracy. For instance, the higher and lower accuracy experiments can correspond to a physical experiment and a computer experiment, respectively.

In this talk, we first review some recent results on the existence of (symmetric) nested orthogonal arrays. Next, some results on the construction of symmetric nested orthogonal arrays are presented. A generalization of symmetric nested orthogonal arrays to asymmetric nested orthogonal arrays is introduced and methods of construction of asymmetric arrays are discussed.