Statistical design of experiments is widely used in scientific and industrial investigations. An optimum orthogonal array can extract as much information as possible at a fixed cost. Finding (optimum) orthogonal arrays is an open (yet fundamental) problem in design of experiments because constructing (optimum) orthogonal arrays or proving non-existence becomes intractable as the number of runs and factors increase. Enumerating orthogonal arrays is equivalent to finding all feasible solutions to a class of inherent…