As an alternative to running all BH trajectories for the same, fixed number of steps, we also implemented a version of the QR-BH search that involves on-the-fly clustering of crystal structures and the termination of BH trajectories that sample the same regions of phase space. In this version, a BH trial is truncated if the new minimum reached from the perturbed structure already exists in the database of structures located thus far. If a BH trajectory is truncated, it is replaced by a new trial initiated from the next unused quasirandom seed in the Sobol sequence, so that the number of active BH trajectories remains constant. To ensure that one BH trajectory is kept active within each region of configurational space, a trajectory is not truncated if it locates a previous structure from its own history and, when two trajectories have located the same structure, the lowest trajectory number (ie. starting from the earliest quasi-random seed) is kept active to continue sampling.