Column expanded Latin hypercube designs

Maximin distance designs and orthogonal designs are extensively applied in computer experiments, but the construction of such designs is challenging, especially under the maximin distance criterion. In this paper, by adding columns to a fold-over optimal maximin $L_2$-distance Latin hypercube design (LHD), we construct a class of LHDs, called column expanded LHDs, which are nearly optimal under both the maximin $L_2$-distance and orthogonality criteria. The advantage of the proposed method is that the resulting designs have flexible numbers of factors without computer search. Detailed comparisons with existing LHDs show that the constructed LHDs have larger minimum distances between design points and smaller correlation coefficients between distinct columns.