Ingrid Carbone introduced the notion of so-called LS-sequences of points, which are obtained by a generalization of Kakutani’s interval splitting procedure. Under an appropriate choice of the parameters $$L$$ and $$S$$ , such sequences have low discrepancy, which means that they are natural candidates for Quasi-Monte Carlo integration. It is tempting to assume that LS-sequences can be combined coordinatewise to obtain a multidimensional low-discrepancy sequence. However, in the present paper, we prove that this is not always the case: if the parameters $$L_1,S_1$$ and $$L_2,S_2$$ of two one-dimensional low-discrepancy LS-sequences satisfy certain number-theoretic conditions, then their two-dimensional combination is not even dense in $$[0,1]^2$$ .