Before revision:  (a) no randomised  algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic  algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic  algorithm that computes a NN with K-2 correct digits using no more than L training samples.
After revision:  (a) no randomised training algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic algorithm that computes a NN with K-2 correct digits using no more than L training samples.