Recursive constructions for covering schemes of strength 3

Abstract

Covering schemes over an abelian group were posed recently in connection with combinatorial arrays such as covering arrays, orthogonal arrays, difference matrices, and difference schemes. This work investigates recursive constructions for covering schemes throughout basic bounds, truncation, reduction, column augmentation, Roux type constructions, and block diagonal construction. Most of the results improve upper bounds and give exact classes for covering schemes of strength 3. Numerical comparison with known upper bounds is discussed in tables for small instances.