In theory, you can make a nuclear explosion as small as you like, right down to a firecracker equivalent! However, you can’t make a nuclear bomb as small as you like.
I’m sure you are familiar with the concept of critical mass. A critical mass of fissile material DOESN’T give you an explosion - it is merely an arrangement of fissile material where the quantity of neutrons generated by fission is exactly equal to the number of neutrons that escape.
To get a fission explosion, you need a supercritical mass, so that the number of neutrons goes up and up and up…The amount of energy you get out of it depends on how long you can maintain supercriticality before the thing blows itself to bits. To get a decent yield you need a large supercriticality, e.g. 2-3 critical masses. And you need to put it together fast, which is what that business with conventional explosives and converging shockwaves is all about.
To get a little fission explosion, you can take a nice Nagasaki-style spherical- implosion plutonium bomb and reduce the amount of explosive in the implosion assembly. When you light it off, instead of getting a 2-3 critical mass supercriticality, aim for 1.001 critical mass, and you will get a satisfying pathetic nuclear explosion.
The trouble with this approach is, it still costs you 1-15kg of plutonium (depending on your bomb design), most of which doesn’t fission at all. It’s very dirty, since all your non-fissioned plutonium is scattered over the neighbourhood. You still have a fairly clunky physical bomb, as opposed to being able to scale it down to grain-of-rice size. And for the size and weight of the thing, you can do better with conventional explosives for taking out the neighbour’s car.
As it goes, the Davy Crockett is pretty small - less that 12 inches diameter and about 60lbs, with a minimum design yield of 10 tonnes TNT equivalent. It’s not at the lower limit, though. Ted Taylor, who did much of the development work for small fission devices in Los Alamos, has been quoted as saying “…less that a kilogram. Quite bit less” when talking about minimum masses of plutonium that can be made to explode. When talking about the smallest bomb that had been produced, he said “It was a full implosion bomb that you could hold in one hand that was about six inches in diameter.” The yield of the thing wasn’t mentioned. (Both quotes from “Project Orion” by George Dyson.)
If you want to take out something a bit bigger than cars but smaller than city blocks (say, a large bridge) then a six-inch nuke with reduced power will have weight and size advantages over the equivalent backpack full of C4, but the cost…