The deterministic investigation of the MTS-TSH implementation presented here indicates that it is possible to recover the main characteristics of a reference calculation using the MTS-TSH algorithm presented in section II B, for example in the case of MTS factor 6. In section III C, we will investigate the possibility to recover statistically relevant quantities from the MTS-TSH algorithm, while in the next section we analyze the speed-ups obtained in the deterministic MTS-TSH simulations.