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Author: Robert Jacobson <[email protected]>

A variety of authors have investigated the benefits of sample pooling to test populations for COVID-19 infection. Of primary interest is reducing the consumption of testing resources, which are a scarce resource during the COVID-19 pandemic, and the accuracy and efficiency of estimating the number of infected individuals. This note discusses the limitations imposed by mathematics on the reduction in number of tests needed to be performed using this testing method and bounds on the number of infected individuals in terms of the number of infected pools. Other limitations related to testing supplies (consumption of pipets, conical tubes, etc.), equipment availability, protocol complexity, and so forth are not discussed. The test for infection is assumed to be 100% effective and 100% sensitive.