I'd recommend a few things here. First, get a roll of chicken wire about three feet wide. Then get some buddies who you can pay with beer and get digging. (Make sure you call the utility companies.) Bury the chicken wire upright all the way around the perimeter of the yard, as close to right under the fence as you can get it. Make sure that when you bury it, you pack the dirt as tightly as you can. This should keep him in the yard.
Next, you need to give him a place where it's okay to dig. You can't get rid of a digging instict, but you can channel it into something less destructive. Go grab some 2x4s, about 4-8 feet long, and use those craftsmen skills to nail them into a square frame. Place the frame on the predetermined sacrificed ground, and go at it with a shovel. Turn up the dirt up to about 3 feet deep. Don't dig it out, just loosen the dirt real good. Let your Dobie (my favorite breed by the way!) watch you do it. Then let him watch you bury some really fun things there; a stuffed Kong, a raw chicken leg, one of those really smelly pig's ears...anything that will pique his interest, especially anything smelly. Bring him over and show him how to dig the treats up. I'm willing to bet he'll get it pretty quickly.
Now you've removed his ability to dig under the fence, and way, WAY more importantly, you've removed his desire to do so. Refill his "toy box" every few days with different fun things. Bury them only in the wooden frame, so he knows this is the only place he should be digging. Remember that variety is the spice of life--be creative!
Last, and just as important, start up some clicker training! Dobies are so, so smart. They need almost constant mental stimulation. Here's a great book to get you going: The Complete Idiot's Guide to Positive Dog Training by Pamela Dennison.