Before revision:  When testing n samples with t tests, as many as k = O(t / \log n) infected samples can be identified at clinically-acceptable false positive and false negative rates.
After revision:  When testing n samples with t tests, as many as k = O(t / \log n) tests when using random binary pooling matrices, with high probability. However, we also use deterministic binary pooling matrices based on combinatorial design ideas of Kirkman Triple Systems to balance between good reconstruction properties and matrix sparsity for ease of pooling. In practice, we have observed the need for fewer tests with such matrices than with random pooling matrices.