Asymmetric Nested Lattice Samples

We propose an approach for constructing asymmetric nested lattice samples by randomizing asymmetric nested orthogonal arrays. Such designs possess a desirable nested structure and have attractive space-filling properties. Unlike recently developed symmetric nested lattice samples, different axes of asymmetric nested lattice samples can be divided at different scales of fineness. The proposed designs are motivated by the problem of running multi-fidelity computer experiments and also are useful for sequential evaluation of complex computer codes, and calibration and validation of computer models.