We give an elementary example, generalizing the one of Bernstein, of a set of pairwise independent random variables which are not jointly independent. It preserves, the "not enough emphasis" characteristic of Bernstein's example in which each random variable is a function of any two of them.
"On a Set of Almost Deterministic $k$-Independent Random Variables." Ann. Probab. 2 (1) 161 - 162, February, 1974. https://doi.org/10.1214/aop/1176996762