We present deep 15.7-GHz observations made with the Arcminute Microkelvin Imager (AMI) Large Array in two fields previously observed as part of the Tenth Cambridge (10C) survey. These observations allow the source counts to be calculated down to 0.1mJy, a factor of five deeper than achieved by the 10C survey. The new source counts are consistent with the extrapolated fit to the 10C source count, and display no evidence for either steepening or flattening of the counts. There is thus no evidence for the emergence of a significant new population of sources (e.g. starforming) at 15.7GHz flux densities above 0.1mJy, the flux density level at which we expect starforming galaxies to begin to contribute. Comparisons with the de Zotti et al. model and the SKADS Simulated Sky show that they both underestimate the observed number of sources by a factor of two at this flux density level. We suggest that this is due to the flat-spectrum cores of radio galaxies contributing more significantly to the counts than predicted by the models.