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Abstract In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $$n$$ items among which $$k$$ are defective, the smallest possible number of tests equals $$\min \{ C_{k,n} k \log n, n\}$$ up to lower-order asymptotic terms, where $$C_{k,n}$$ is a uniformly bounded constant (varying depending on the scaling of $$k$$ with respect to $$n$$) with a simple explicit expression. The algorithmic upper bound follows from a minor adaptation of an existing analysis of the Definite Defectives algorithm, and the algorithm-independent lower bound builds on existing works for the regimes $$k \le n^{1-\varOmega (1)}$$ and $$k = \varTheta (n)$$. In sufficiently sparse regimes (including $$k = o\big ( \frac{n}{\log n} \big )$$), our main result generalizes that of Coja-Oghlan et al. (2020) by avoiding the assumption $$k \le n^{1-\varOmega (1)}$$, whereas in sufficiently dense regimes (including $$k = \omega \big ( \frac{n}{\log n} \big )$$), our main result shows that individual testing is asymptotically optimal for any non-zero target success probability, thus strengthening an existing result of Aldridge (2019, IEEE Trans. Inf. Theory, 65, 2058–2061) in terms of both the error probability and the assumed scaling of $$k$$.