  Contact interactions can be used to describe a system of particles at
unitarity, contribute to the leading part of nuclear interactions and are
numerically non-trivial because they require a proper regularization and
renormalization scheme. We explain how to tune the coefficient of a contact
interaction between non-relativistic particles on a discretized space in 1, 2,
and 3 spatial dimensions such that we can remove all discretization artifacts.
By taking advantage of a latticized L\"uscher zeta function, we can achieve a
momentum-independent scattering amplitude at any finite lattice spacing.
