  The overlap hypercube fermion is a variant of a chirally symmetric lattice
fermion, which is endowed with a higher level of locality than the standard
overlap fermion. We apply this formulation in quenched QCD simulations with
light quarks. In the p-regime we evaluate the masses of light pseudoscalar and
vector mesons, as well as the pion decay constant and the renormalisation
constant Z_A. In the epsilon-regime we present results for the leading Low
Energy Constants of the chiral Lagrangian, Sigma and F_pi. To this end, we
perform fits to predictions by chiral Random Matrix Theory and by different
versions of quenched Chiral Perturbation Theory, referring to distinct
correlation functions. These results, along with an evaluation of the
topological susceptibility, are also compared to the outcome based on the
standard overlap operator.
