Construction of nested orthogonal arrays of parallel-flats type

- The nested orthogonal arrays of parallel-flats type is proposed for multi-fidelity computer experiments.
- Theoretical results for design construction are developed.
- A catalogue of nested orthogonal arrays is provided for practical applications.

Recently, construction of nested orthogonal arrays receives notable attention, which serves as a stepping stone for planning deterministic computer simulations with various levels of accuracy. In this article, a new class of nested orthogonal arrays called the nested orthogonal arrays of parallel-flats type is introduced for addressing this interesting issue. Firstly, sufficient and necessary condition is presented for constructing the proposed designs, and a new collection of nested orthogonal arrays is then explicitly characterized. Furthermore, a heuristic algorithm is devised to search the proposed designs with small to moderate run-sizes, and some analytical methods are developed for generating large designs through existing small ones. For a given number of input variables of interest, a series of the proposed designs with various run-sizes is obtained and collected in a catalogue. This offers a reference for a practitioner to plan a two-fidelity computer experiment. This article has supplementary materials online.