  Based on work of P. Balister, B. Bollob\'as, R. Morris, J. Sahasrabudhe and
M. Tiba, we show that if a covering system has distinct squarefree moduli, then
the minimum modulus is at most 118. We also show that in general the $k^{\rm
th}$ smallest modulus in a covering system with distinct moduli (provided it is
required for the covering) is bounded by an absolute constant.
