Exact expressions for the maximal probability that all k-wise independent bits are 1

Let M(n, k, p) denote the maximum probability of the event X_1 = X_2 = \cdots = X_n=1 under a k-wise independent distribution whose marginals are Bernoulli random variables with mean p. A long-standing question is to calculate M(n, k, p) for all values of n,k,p. This question has been... Show more