A strictly stationary, NN-tuplewise independent counterexample to the Central Limit Theorem

For an arbitrary integer N≥2N≥2, this paper gives the construction of a strictly stationary (and ergodic), NN-tuplewise independent sequence of (nondegenerate) bounded random variables such that the Central Limit Theorem fails to hold. The sequence is in part an adaptation of a nonstationary example with similar properties constructed by one of the authors (ARP) in a paper published in 1998.