The existence of odd covering system with distinct moduli is a famous open question proposed by Erdős and Selfridge.

I wonder whether a restricted condition for the problem that odd covering system without modulus 3 is also an open problem. That is to say, whether an incongruent covering system with the minimum modulus greater than 3 and whose moduli are odd exist or not.

Thanks.

p.s. The same question was posted on MSE. If I get an answer from one site I would delete the other.