Let k=k(n) be the largest integer such that there
exists a k-wise uniform distribution over \zo^n that
is supported on the set S_m := \{x \in \zo^n : \sum_i x_i \equiv 0 \bmod m\}, where m is any integer. We
show that $\Omega(n/m^2 \log m) \le k \le 2n/m + ... more >>>