I don't have personal experiece with keeping rabbits out of the garden, but found this online.

"Use chicken wire with one-inch or smaller mesh as shown in the
illustration at the top of the page, fencing should be at least 2 feet
high to prevent rabbits from jumping over. To keep them from burrowing
under, bury at least 3 to 6 inches (the deeper the better) and bend the
buried portion away from plantings. Be sure to inspect fencing
frequently to make sure rabbits haven’t created an opening."

From: Keeping rabbits out of the garden

Unfortunately the unanswered posts don't stay at the top like they used to so I'm reviving a couple in hopes that they will get the response that they deserve.

Original home owner poured this ~5 inch wide and 3 to 4 inch thick concrete barrier along the fence line:

No base but the clay, no steel reinforcement, variable thickness, and poor tooling... but it's working well into it's fifth decade. Just a few cracks and a couple foot section that crumbled when the dirt mover drove across it while digging the pool. Looks like he mixed it up a bag or two at a time and poured it in post-to-post segments. Though not sure this is necessary.

The more important part of the rabbit barrier is the treated lumber that runs across the bottom of the fence pickets. It's 3 or 4 inches into the soil on the opposite side depending on the contour. In fact, this alone (no concrete) seems to keep the rabbits out of our side yard:

The second photo shows a small section of the side yard fence that also has a galvanized flashing barrier down to 8 or 10 inches - however, that's to keep the canna lilies in bounds rather than the rabbits out.

We still get a lot of rabbit damage in the front and alley, but haven't been getting any in the side yard since we fenced it this way. Seems a wood barrier only about 3 inches into the clay is enough to keep our local rabbits out. We've been getting at least 20 years out of the treated lumber with this kind of soil contact on our well draining lot.

If you find they still dig under a shallow wood barrier, you can always add depth later by attaching flashing or chicken wire to the lumber as we did for the cannas.

We use concrete, stone, or timbers with small gaps to the fencing to keep them out at the gates.