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We propose two methods for constructing a new type of design,called a nested orthog-onal array-based Latin hypercube design,intended for multi-fidelity computer experiments.Such designs are two nested space-filling designs in which the large design achieves stratification in both bivariate and univariate margins and the small design achieves stratification in univariate margins.These designs have better space-filling properties than nested Latin hypercube designs in which the large design possesses uniformity in univariate margins only.The first method expands an ordinary Latin hypercube design to a larger design that achieves uniformity in any one-or two-dimensional projection.The second method uses an orthogonal array with strength two to simultaneously con-struct a pair of nested orthogonal array-based Latin hypercube designs.Examples are given to illustrate the proposed methods.Sampling properties of the proposed designs are derived.