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.