A quenched study of m_b in HQET beyond the leading order

A non perturbative method to compute the mass of the b quark including the 1/m term in HQET has been presented in a companion talk. Following this strategy, we find in the MS bar scheme m_b^{stat}(m_b) = 4.350(64) GeV for the leading term, and m_b^{(1)}(m_b) = -0.049(29) GeV for the next to leading order correction. This method involves several steps, including the simulation of the relativistic theory in a small volume, and of the effective theory in a big volume. Here we present some numerical details of our calculations.