We demonstrate that the inclusion of a BCS importance function dramatically increases the efficiency of the auxiliary field method for strong pairing. We calculate the ground-state energy of an unpolarized fermi gas at unitarity with up to 66 particles and lattices of up to 27^3 sites. The method has no fermion sign problem, and an accurate result is obtained for the universal parameter ξ. Several different forms of the kinetic energy adjusted to the unitary limit but with different effective

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... nges extrapolate to the same continuum limit within error bars. The finite effective range results for different interactions are consistent with a linear term proportional to the Fermi momentum times the effective range. The new method described herein will have many applications in superfluid cold atom systems and in both electronic and nuclear structures when pairing is important.