Just wanted to say I feel your pain. My pup is a digger too! What has worked best is that he is never unsupervised. If he even looks like he's going to dig I remove him from the area and tell him no.
Change the GAME & your tolerance level of unacceptable actions.I never let her out of my sight but she is quick. In the few seconds it took for me to get to her in the yard she had dug a pretty decent hole. She is going through a destructive phase. She has grabbed the mobile phone and the remote and although both still work they have bite marks on them. She thinks it is all a game. I will try the suggestions posted. Thank you.