Fig 2. Two-Dimensional pooling example.

A total of 96 samples are arrayed in symmetrical 5x5 grids (with 4 empty wells in the last grid) and k = 9 of the samples are positive (red wells). The pooling procedure combines each row and each column of a grid into separate pools for a total of T = 2 × 5 × 4 = 40 tests. Samples that are at the intersection of a positive row and a positive column (marked with an “X”) are potentially positive samples. When more than one row and more than one column are positive, some of the samples at the intersections are likely false positives (e.g. the top left and bottom right grids). Otherwise, the results are unambiguous and the correct positive samples can be identified (e.g. the top right and bottom left grids).