Looking for a large trunk bag
I have a rear trunk bag made by Jandd that's pretty satisfactory, with side pockets I find useful. It attaches to well to any rear rack with easy Velcro straps. There are a couple features on more expensive bags that I would mention. First is an attached rain cover that stows away when not in use. I use a simple plastic bag with handles, secured by two of the diagonally opposed straps and that has worked fine for me, even in heavy rain.
Secondly are drop down bags, like mini-panniers, that are useful to store extra clothing, like a jacket, as you remove it during a ride. (On a long ride I bring my own food and water so the trunk is usually full.) For my bag I use a bungee cord to hold down the extra clothing, though one has to be careful it is well-secured and nothing flaps into the spokes or chain.