  We present a determination of nucleon-nucleon scattering phase shifts for l
>= 0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet
channels are computed with lattice Quantum ChromoDynamics. For l > 0, this is
the first lattice QCD calculation using the Luscher finite-volume formalism.
This required the design and implementation of novel lattice methods involving
displaced sources and momentum-space cubic sinks. To demonstrate the utility of
our approach, the calculations were performed in the SU(3)-flavor limit where
the light quark masses have been tuned to the physical strange quark mass,
corresponding to m_pi = m_K ~ 800 MeV. In this work, we have assumed that only
the lowest partial waves contribute to each channel, ignoring the unphysical
partial wave mixing that arises within the finite-volume formalism. This
assumption is only valid for sufficiently low energies; we present evidence
that it holds for our study using two different channels. Two spatial volumes
of V ~ (3.5 fm)^3 and V ~ (4.6 fm)^3 were used. The finite-volume spectrum is
extracted from the exponential falloff of the correlation functions. Said
spectrum is mapped onto the infinite volume phase shifts using the
generalization of the Luscher formalism for two-nucleon systems.
