In this article, we propose a fast and precise method of calculating a theoretically maximum metamer mismatch volume. Unlike earlier proposed techniques, our method does not use any assumptions on the shape of spectra on the boundary of the mismatch volume. The method utilises a spherical sampling approach and a linear programming optimisation. Experiments described in this paper show that under certain conditions the theoretically maximum metamer mismatch volume is significantly larger than the one approximated using previous method that makes assumptions about the shape of the spectra.