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Suppressing SARS-CoV-2 will likely require the rapid identification and isolation of infected individuals, on an ongoing basis. RT-PCR (reverse transcription polymerase chain reaction) tests are accurate but costly, making regular testing of every individual expensive. The costs are a challenge for all countries and particularly for developing countries. Cost reductions can be achieved by combining samples and testing them in groups. We propose an algorithm for grouping subsamples, prior to testing, based on the geometry of a hypercube. At low prevalence, this testing procedure uniquely identifies infected individuals in a small number of tests. We discuss the optimal group size and explain why, given the highly infectious nature of the disease, parallel searches are preferred. We report proof of concept experiments in which a positive sample was detected even when diluted a hundred-fold with negative samples. Using these methods, the costs of mass testing could be reduced by a factor of ten to a hundred or more. If infected individuals are quickly and effectively quarantined, the prevalence will fall and so will the costs of regularly testing everyone. Such a strategy provides a possible pathway to the longterm elimination of SARS-CoV-2. Field trials of our approach are now under way in Rwanda and initial data from these are reported here. * nturok@perimeterinstitute.ca † wndifon@nexteinstein.org . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)