In my youth I did a bunch of neolithic camping.
But now my minimum sleeping gear is a small tarp made out of ripstop nylon that I have waterproofed and a bag that I have made out of rip stop nylon that I fill with leaves and grass to sleep on.
I carry both of these things in a zip lock bag and they take up almost no room. I have sewn loops on the corners and the sides so don't forget the twine to hold them up.
Don't use grommets because they tend to pull out in the wind....