  The intriguing search for permutations that generate generalised van der
Corput sequences with exceptionally small discrepancy forms an important part
of the research work of Henri Faure. On the occasion of Henri's 80th birthday
we aim to survey (some of) his contributions over the last four decades which
considerably improved our understanding of one-dimensional van der Corput
sequences and inspired a lot of related work. We recall and compare the
different approaches in the search for generalised van der Corput sequences
with low discrepancy, i.e., using a single generating permutation versus using
a sequence of permutations. Throughout, we collect, sharpen and extend open
questions which all stem from the extensive work of Henri and his coworkers and
which will hopefully inspire more work in the future.
