How to make a run fox-proof. Foxes are challenging as they dig and can climb a wire fence. Start by deciding how big you will make the run. There are a lot of different ways to build it. You can just use fence posts and wire or you can frame it like JT did in his photo above. If you are going to frame it look at the length of building materials available and plan the size around those. You might look at the length of a roll of wire also.
There are a lot of different types of wire available. The heavier (smaller) the gauge of the wire and the smaller the openings the more critters it will stop. I don't know where you are located or what predators other than foxes you might have, for a lot of people dogs are a big threat and dogs can get pretty big. A large dog or even a large boar raccoon can tear lighter gauges of chicken wire and even some hardware cloth. How it is attached is important too. A lot of failures are due to fasteners tearing out instead of the wire tearing.
There are different reasons to look at the size of your openings in the wire. One obvious one is that the bigger the hole the more critters can go through. The smaller the opening the harder it might be for a big critter to get a grip to pull on it. And it sounds like you have bantams. Can bantams or maybe bantam chicks get through the openings?
To stop foxes or other critters from digging I suggest you use an apron. Lay a piece of wire mesh maybe 18" to 24" wide around the outside of your run and attach that to the bottom of the run well enough that you don't have openings a critter can get through. You can use piece of wire, hog rings, or maybe J-clips to attach that wire. If the bottom of your run is a solid piece of wood you can attach the apron to that. I prefer putting a piece of wood over the wire and screwing it on but there are other ways to attach it.
You don't have to bury your apron, just lay something on top of it to hold it down until grass grows through it, the grass will hold it down. But I like to take the turf off, maybe 2" deep will do it, and put that back on top to keep the wire out of the way of mowers and especially weed whackers. Instead of attaching a piece of wire you can bend your wire fencing with a 90 degree angles at the bottom. The idea is that a critter goes up to your fence, starts digging, hits the wire, and doesn't know to back up. It is really effective.
Since a fox can climb it needs a top. I strongly urge you to build it tall enough so you can easily walk in there without bumping your head. Strongly urge. You have many different ways to cover it. A solid roof sloped to take rainwater away from your run can help keep it dry and provide shade but remember that water and sunlight can come in from the side. Still, a solid roof has many benefits.
If you use wire for a top it needs to be prevented from sagging. There are different ways to do that depending n how wide that run is and what your sides look like. The wider that span the heavier and stronger your support needs to be. It may need to support a build up of leaves if trees are nearby. Snow and ice can possibly build up, depending where you are. Those can get heavy.
You have so many options for any of this it's hard to be specific. If you can give us some ideas of what you are thinking we may be able to be a lot more specific with ideas. It can be a good idea to let us look at your design before you build it or buy materials. Good luck, hope you enjoy your move once it is over with.
