Fig. 3: Expected number of tests per person, to find all individuals who are infected, using the hypercube algorithm.

The results are shown on a log–log plot. The dashed grey line shows epln(0.734/p), the result obtained in the large D approximation, for which the optimal group size N ≈ 0.35/p. The coloured lines show the results obtained from a detailed analysis when the group size N = 3^D with D an integer. Where 0.35/p is an exact power of 3, as at the left end of each coloured curve, optimal performance is attained. As p is increased, a growing fraction of sites in the 3^D hypercube are left empty, until 0.35/p is again an exact power of 3 (Supplementary Information).