Strongly Explicit and Efficiently Decodable Probabilistic Group Testing

We consider the non-adaptive probabilistic group testing problem where d random defective items are identified with high probability from a population of N items by applying t binary group tests. There has been recent progress towards developing explicit and efficiently decodable group testing schemes with t = Θ(dlogN) tests, which is known to be order-optimal for this setting when d = O(N
^1-α
) for some constant α > 0. In particular, a recent work develops an explicit scheme while another one develops an efficiently decodable scheme for this setting, both with the order-optimal t = Θ(dlogN) tests. However, to the best of our knowledge, there is no order-optimal scheme that is both explicit and efficiently decodable. In this paper, we close this gap by introducing the first (strongly) explicit and efficiently decodable construction that is order-optimal for the non-adaptive probabilistic group testing problem.