  Covering systems were introduced by Erd\H{o}s in 1950. In the same article
where he introduced them, he asked if the minimum modulus of a covering system
with distinct moduli is bounded. In 2015, Hough answered affirmatively this
long standing question. In 2022, Balister, Bollob\'as, Morris, Sahasrabudhe and
Tiba gave a simpler and more versatile proof of Hough's result. Building upon
their work, we show that there exists some absolute constant $c>0$ such that
the $j$-th smallest modulus of a minimal covering system with distinct moduli
is $\le \exp(cj^2/\log(j+1))$.
