Optimal resolvable 2 x c grid-block Coverings

Abstract

The notion of grid-block designs was introduced by Fu et al.[J. Statist. Plann. Inference, 119(2):225-236, 2004] for the applications to DNA library screenings based on non-Adaptive group testing. This paper is concentrated on resolvable grid-block coverings with a minimal number of parallel classes, which are called optimal. In particular, we characterize optimal 2 x c resolvable coverings, and prove that an optimal resolvable 2x3 covering of order v exists if and only if v = 0 (mod 6). © 2015 Utilitas Mathematics.