Before revision:  We prove that  our multilevel EnKBF can achieve a mean square error (MSE) of O(\epsilon^2), \ \epsilon>0 with a cost of order O(\epsilon^{-2}\log(\epsilon)^2).
After revision:  We prove that an ideal version of our multilevel EnKBF can achieve a mean square error (MSE) of O(\epsilon^2), \ \epsilon>0 with a cost of order O(\epsilon^{-2}\log(\epsilon)^2).