  Low discrepancy point sets have been widely used as a tool to approximate
continuous objects by discrete ones in numerical processes, for example in
numerical integration. Following a century of research on the topic, it is
still unclear how low the discrepancy of point sets can go; in other words, how
regularly distributed can points be in a given space. Recent insights using
optimization and machine learning techniques have led to substantial
improvements in the construction of low-discrepancy point sets, resulting in
configurations of much lower discrepancy values than previously known. Building
on the optimal constructions, we present a simple way to obtain
$L_{\infty}$-optimized placement of points that follow the same relative order
as an (arbitrary) input set. Applying this approach to point sets in dimensions
2 and 3 for up to 400 and 50 points, respectively, we obtain point sets whose
$L_{\infty}$ star discrepancies are up to 25% smaller than those of the
current-best sets, and around 50% better than classical constructions such as
the Fibonacci set.
