  We develop ultratransferable pseudopotentials for the contact interaction
that are 100 times more accurate than contemporary approximations. The
pseudopotential offers scattering properties very similar to the contact
potential, has a smooth profile to accelerate numerics by a factor of up to
4,000, and, for positive scattering lengths, does not support an unwanted bound
state. We demonstrate these advantages in a Diffusion Monte Carlo study of
fermions with repulsive interactions, delivering the first numerical evidence
for the formation of a p-wave superconducting state.
