Used the plastic deer netting as well. I've always had rabbits in my garden but they've never done noticeable damage so we coexist. Unfortunately, they easily chew holes in the netting and once the hens find the holes, it's over
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Update: I added either 2 or 3 strands of 17 gauge aluminum wire to the top of my 4 ft picket fence. This solved the problem in several ways.
First, because the birds would hop onto the fence posts and then hop down, the new additions to the tops of the posts block them from landing on the top of fence post. Second, if they try to fly right over the fence they hit the wire and harmlessly fall back (it's not electrified). The wire is too thin for them to see well so they aim for the picket fence and don't realize there's another 7-10 inches of clearance needed to get over the wire. I saw this happen once and I admit it was kinda funny. The chicken had no idea what she hit and kept pacing up and down staring at the top of the fence but unable to understand what she'd hit.
I also added height to the two gates to the garden to close up those gaps, too. It was a good three days work but my garden has been chicken free for several days now and I'm relieved.