Constructions of Optimal Sparse r‐Disjunct Matrices via Packings

ABSTRACT Group testing has been widely used in various aspects, and the ‐disjunct matrix plays a crucial role in group testing. The original purpose of the group testing is to identify a set of at most positive items from a batch of total items using as fewer tests as possible. In many practical applications, each test can include only a limited number of items and each item can participate in a limited number of tests. In this paper, we use the tools from combinatorial design theory to construct optimal 2‐disjunct matrices with rows and limited row weight and optimal 3‐disjunct matrices with rows and limited row weight , respectively. Also we use the known graph‐matching theorem to give an asymptotically optimal upper bound on the ‐disjunct matrices with limited column weight .