Was the wire they got through chicken wire / poultry netting? It is generally observed that chicken wire will turn chickens, but will not deter a determined predator. I mention this for your benefit, but also for any and all others who might be thinking chicken wire is good enough. It's not. Lots of things can get through chicken wire.
Depending on the amount of coverage needed and predator list, you can start with 1/2" hardware cloth, or upgrade to the more sturdy deterrent of 1/2" x 1" welded wire, 1" x 2" welded wire at the coop / run level. Anything larger than 1" will permit weasels and such a way in. About the only difference between 1" x 2" and 2" x 4" is the cost. For a really large run or coverage area, that may add up enough to matter, but while 2" x 4" fence will deter large predators, the smaller ones can get through it. You can always double it up along the bottom, but is it cheaper to use 1" x 2" to start with, or 2" x 4" with chicken wire or hardware cloth over it? My house has 1/2" x 1" - 14 gauge welded wire and varmints are outside it all the time, but they don't get in.
But in any event, the ultimate safety comes from a really tight coop at ground zero, no holes larger than 1" anywhere and made of sturdy stuff. Goal is when the lights go dim at dusk, the birds go to roost where they are safe for the night. Their house will protect them from nearly all threats and things that go bump in the night. Then at the perimeter of your pasture / free range area, an electric fence to keep most predators well away from them to begin with.
