  This note addresses the question of the number of normalizable vacuum states
in supersymmetric quantum mechanics with sixteen supercharges and arbitrary
semi-simple compact gauge group, up to rank three. After evaluating certain
contour integrals obtained by appropriately adapting BRST deformation
techniques we propose novel rational values for the bulk indices. Our results
demonstrate that an asymptotic method for obtaining the boundary contribution
to the index, originally due to Green and Gutperle, fails for groups other than
SU(N). We then obtain likely values for the number of ground states of these
systems. In the case of orthogonal and symplectic groups our finding is
consistent with recent conjectures of Kac and Smilga, but appears to contradict
their result in the case of the exceptional group G_2.
