  This paper adresses the question whether the $LS$-sequences constructed by
Carbone yield indeed a new family of low discrepancy sequences. While it is
well known that the case $S=0$ corresponds to van der Corput sequences, we
prove here that the case $S=1$ can be traced back to two-sided Kronecker
sequences and moreover that for $S \geq 2$ none of these two types occurs
anymore. In addition, our approach allows for an improved discrepancy bound for
$S=1$ and $L$ arbitrary.
