Exact Values and Bounds on Covering Schemes of Strength Two

ABSTRACT In this work, we investigate covering schemes of strength 2 over finite abelian groups, establishing new lower and upper bounds and evaluating new exact values. A main result is a new general lower bound that improves the trivial one and achieves optimality for the binary case. We also develop a recursive relation based on subsets of the group with a specific property, which generalizes a recent result by Shokri and Moura and highlights the structural role of the group. Connections with graph theory are explored, allowing fundamental parameters to be reinterpreted and new exact values to be obtained through computational methods. Finally, we analyze the open case of covering schemes of strength 2 with five columns, deriving new general upper bounds. In particular, based on constructions of holey difference matrices by Ding and Yin, near‐exact values are obtained.