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

An upper bound for the minimum modulus in a covering system with squarefree moduli