Let X_{m, \eps} be the distribution over m bits (X_1, \ldots, X_m)
where the X_i are independent and each X_i equals 1 with
probability (1+\eps)/2 and 0 with probability (1-\eps)/2. We
consider the smallest value \eps^* of \eps such that the distributions
X_{m,\eps} and X_{m,0} can be distinguished with constant
advantage by a function f : \{0,1\}^m \to S which is the product of k
functions f_1, f_2, \ldots, f_k on disjoint inputs of n bits, where each
f_i : \{0,1\}^n \to S and m = nk.

We prove that \eps^* = \Theta(1/\sqrt{n \log k}) if S = \{0,1\} and if S = \{-1,1\}, while \eps^* = \Theta(1/\sqrt{nk}) if S is the set of
unit-norm complex numbers.