If you have raccoons or fishers in your area I wouldn't use anything less than hardware cloth to cover the whole thing and a foot and a half down into the soil. I've had raccoons rip apart light gauge welded wire in the past. In my neck of the woods, using chicken wire or deer netting is little better than using nothing.
You can get by with a maximum security run if you close up the birds in a 100% secure coop every night. My hens have constant access to the run so a predator that rips through chicken wire or netting could walk right into the coop. I've lost birds this way in the past and the flock of 12 birds I gave away this past spring was eaten because of that. (I had my doubts those birds were going to survive but I let them go anyway. I learned the hard way to never give anyone a chicken that looks doomed to become critter food because of flimsy protection.)
So I opted for a cattle panel frame covered with 1/2" hardware cloth and, as mentioned, buried 18" into the ground.
Granted, the value of the eggs may mean I break even on the cost of the maximum security run in about 2011, but no critter short of a raccoon with an acetylene torch will break into the run. (Unless it's a fisher with a chainsaw going in via the coop.)
Wayne
