A new and flexible method for constructing designs for computer experiments.

*(English)*Zbl 1190.62141Summary: We develop a new method for constructing “good” designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of orthogonal Latin hypercubes and obtain many results along the way. In terms of run sizes, the existence problem of orthogonal Latin hypercubes is completely solved. We also present an explicit result showing how large orthogonal Latin hypercubes can be constructed using small orthogonal Latin hypercubes. Another appealing feature of our method is that it can easily be adapted to construct other designs; we examine how to make use of the method to construct nearly orthogonal and cascading Latin hypercubes.

##### MSC:

62K99 | Design of statistical experiments |

05B15 | Orthogonal arrays, Latin squares, Room squares |

62P99 | Applications of statistics |

05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |

##### Keywords:

cascading Latin hypercube; Hadamard matrix; Kronecker product; orthogonal array; orthogonal Latin hypercube; space-filling design##### Software:

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\textit{C. D. Lin} et al., Ann. Stat. 38, No. 3, 1460--1477 (2010; Zbl 1190.62141)

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