We investigate \(L_2\) -discrepancies of what we call weak Latin hypercubes. In this case it turns out that there is a precise equivalence between the extreme and periodic \(L_2\) -discrepancy which follows from a much broader result about generalized energies for weighted point sets. Motivated by this we study the asymptotics of the optimal \(L_2\) -discrepancy of weak Latin hypercubes. We determine asymptotically tight bounds for \(d \ge 3\) and even the precise (dimension dependent) constant in front of the dominating term for \(d \ge 4\) .
