Overlap hypercube fermions in QCD with light quarks

We report on simulation results with overlap hypercube fermions (overlap HF) - a type of exactly chiral lattice fermions - and their link to chiral perturbation theory. We first sketch the construction of the overlap HF and discuss its high level of locality. Next we show applications in the p-regime of QCD, where we evaluate m_{\pi}, m_{\rho}, the quark mass according to the PCAC relation, the renormalisation constant Z_A and the pion decay constant F_{\pi} as functions of the bare quark mass. F_{\pi} is then reconsidered at even smaller quark masses in the epsilon-regime, along with the scalar condensate \Sigma. In that context we also discuss results for the topological charges and susceptibility.