LAUSR

Group testing has been widely used in various aspects, and the r ‐disjunct matrix plays a crucial role in group testing. The original purpose of the group testing is to identify a set of at most r positive items from a batch of M 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 n rows and limited row weight 3 < ρ ≤ ⌊ n − 1 2 ⌋ and optimal 3‐disjunct matrices with n rows and limited row weight 4 < ρ ≤ ⌊ n − 1 3 ⌋ , respectively. Also we use the known graph‐matching theorem to give an asymptotically optimal upper bound on the r ‐disjunct matrices with limited column weight r + 1 ≤ w ≤ 2 r .