Performance of Group Testing Algorithms With Near-Constant Tests-per-Item

We consider the nonadaptive group testing with N items, of which K = Θ(Nθ) are defective. We study a test design in which each item appears in nearly the same number of tests. For each item, we independently pick L tests uniformly at random with replacement, and place the item in those tests. We analyse the performance of these designs with simple and practical decoding algorithms in a range of sparsity regimes, and show that the performance is consistently improved in comparison with standard Bernoulli designs.We show that our new design requires roughly 23% fewer tests than a Bernoulli design when paired with the simple decoding algorithms known as COMP and DD. This gives the best known nonadaptive group testing performance for θ > 0:43, and the best proven performance with a practical decoding algorithm for all θ ∈ (0, 1). We also give a converse result showing that the DD algorithm is optimal with respect to our randomised design when θ > 1/2. We complement our theoretical results with simulations that show a notable improvement over Bernoulli designs in both sparse and dense regimes.