Some classes of orthogonal Latin hypercube designs

Ifigenia Efthimiou · S. Georgiou

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Optimal Experimental Design Methods Advanced Combinatorial Mathematics Mathematical Approximation and Integration

Abstract

Latin hypercube designs (LHDs) are popularly used in designing computer experiments. A number of methods have been proposed to construct LHDs with orthogonality among the main-effects. In this paper, we propose a new method for constructing orthogonal LHDs (OLHDs) with 12, 16, 20 and 24 factors having a flexible run size. Moreover, using the new designs presented in this paper, we provide new multiplication methods and further constructions for OLHDs. These constructions lead to new infinite families of OLHD with many factors. For example, we show that when an OLHD(n;m) exists then there also exist OLHDs with (runs; factors) 2 f(24n; 12m), (32n; 16m), (40n; 20m), (48n; 24m), (24n+1; 12m), (32n+1; 16m), (40n+1; 20m), (48n+1; 24m)g. The constructed classes of OLHD are new and are given in this paper for the first time.

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References

1998Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments 2006A construction method for orthogonal Latin hypercube designs 2009Construction of orthogonal Latin hypercube designs 2001Optimal and orthogonal Latin hypercube designs for computer experiments 2010Construction of orthogonal Latin hypercube designs with flexible run sizes 2008Orthogonal Latin hypercube designs from generalized orthogonal designs

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2014Column-orthogonal strong orthogonal arrays and sliced strong orthogonal arrays 2019Construction results for strong orthogonal arrays of strength three 2018On the connection between maximin distance designs and orthogonal designs

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