Chemically speaking, random means uniform. As to whether there could be an infinite number of laws, that would be equivalent to having an infinite number of dimensions. With an infinite number of dimensions you could have an infinite number of contradictions, yet since that is an artificiality from mixing dimensions, the universe would still operate as it does. Our concepts are very much simpler than reality; an infinitude of laws would, in fact, decribe reality rather than just a scientific lab experiment.
Our concepts would have to be much simpler than reality, if reality is comprised of an infinite number of dimensions, while we humans are pretty much stuck with three of space and one of time, making four. That would be a very severe handicap for human understanding -- so severe, in fact, that I'd wonder how a scientist could even summon the will to get out of bed in the morning, knowing his entire day will be spent in an exercise in virtual futility....
Thanks for the tip re: random = uniform = chaos??? I suppose this interesting problem you raise might be soluable if we propose that most dimensions "extra" to our own normal perceptive apparatus could hang out in "imaginary time" -- like the "extra" dimensions of string theory.... But working out the details looks like it'd be a whole lot of work to me.... Apparently, it's already hard enough WRT the 11 dimensions of string theory....
Alternatively, one could simply take the "theist's way out" and simply assume that God would not have made a world that man would find very difficult to understand. Oooooppss! My anthropocentrism is showing....