  Necessary and sufficient conditions for the square-integrability of recently
proposed unbiased estimators are established. A geometric characterization of a
distribution that optimizes the performance of these estimators is given. An
algorithm based on convex hulls that finds the optimal distribution truncated
to its first m terms in time linear in m is described. The algorithm exploits a
connection with a recent randomized dimension reduction method and is
illustrated via a numerical example.
