Construction of nearly orthogonal Latin hypercube designs

The Latin hypercube design (LHD) is a popular choice of experimental design when computer simulation is used to study a physical process. In this paper, we propose some methods for constructing nearly orthogonal Latin hypercube designs (NOLHDs) with 2, 4, 8, 12, 16, 20 and 24 factors having flexible run sizes. These designs can be very useful when orthogonal Latin hypercube designs (OLHDs) of the needed sizes do not exist.