Bounds for the Minimum Distance and Covering Radius of Orthogonal Arrays Via Their Distance Distributions

We study the packing and covering properties of orthogonal arrays (OAs) as we propose new approaches for obtaining estimations on the minimum distance and covering radius of orthogonal arrays (designs) via examination of their distance distributions. First, we use some special representation of a linear system of equations which allows us to analyse extreme solutions (distance distributions). Second, we show how databases with (feasible) distance distributions can be used for obtaining sharp bounds for the minimum distance and covering radius of OAs. Correspondingly, new bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of OAs.