  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.
