  In [Mas82] and [Vee78] it was proved independently that almost every interval
exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem
implies that these maps mainly have uniformly distributed orbits. This raises
the question under which conditions the orbits yield low-discrepancy sequences.
The case of $n=2$ intervals corresponds to circle rotation, where conditions
for low-discrepancy are well-known. In this paper, we give corresponding
conditions in the case $n=3$. Furthermore, we construct infinitely many
interval exchange transformations with low-discrepancy orbits for $n \geq 4$.
We also show that these examples do not coincide with $LS$-sequences if $S \geq
2$.
