Edit: I've once thought of a system which would allow virtually unlimited compression, the only drawback is that it would take an insane amount of time to execute.
Imagine a chess board, a 8x8 grid of alternating black and white tiles. Now you write an algorithm that performs permutations, 2 by 2, 4 by 4, etc, in a predefined order.
If you do enough permutations, at some point you're going to have all the white tiles on one side of the board, and the black ones on the other side.
You can now store your board as its size, 2 expressions representing the 2 halfs, and the number of permutations you need to reach the original state.
Looking forward to additional info on this joke/hoax!