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Suppressing infections of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) will probably require the rapid identification and isolation of individuals infected with the virus on an ongoing basis. Reverse-transcription polymerase chain reaction (RT-PCR) tests are accurate but costly, which makes the regular testing of every individual expensive. These costs are a challenge for all countries around the world, but particularly for low-to-middle-income countries. Cost reductions can be achieved by pooling (or combining) subsamples and testing them in groups 1-7 . A balance must be struck between increasing the group size and retaining test sensitivity, as sample dilution increases the likelihood of false-negative test results for individuals with a low viral load in the sampled region at the time of the test 8 . Similarly, minimizing the number of tests to reduce costs must be balanced against minimizing the time that testing takes, to reduce the spread of the infection. Here we propose an algorithm for pooling subsamples based on the geometry of a hypercube that, at low prevalence, accurately identifies individuals infected with SARS-CoV-2 in a small number of tests and few rounds of testing. We discuss the optimal group size and explain why, given the highly infectious nature of the disease, largely parallel searches are preferred. We report proof-of-concept experiments in which a positive subsample was detected even when diluted 100-fold with negative subsamples (compared with 30-48-fold dilutions described in previous studies 9-11 ). We quantify the loss of sensitivity due to dilution and discuss how it may be mitigated by the frequent re-testing of groups, for example. With the use of these methods, the cost of mass testing could be reduced by a large factor. At low prevalence, the costs decrease in rough proportion to the prevalence. Field trials of our approach are under way in Rwanda and South Africa. The use of group testing on a massive scale to monitor infection rates closely and continually in a population, along with the rapid and effective isolation of people with SARS-CoV-2 infections, provides a promising pathway towards the long-term control of coronavirus disease 2019 (COVID-19).