Smart random generated 2D array?

Hey so I am looking to generate a smart random 2D array. What do I mean? Well smart random number generation is when you generate numbers that are not non-repeating, but does not repeat soon after being generated.

This technique is pretty available and is often used in for example, generating random music playlists. However, what I am looking for is to have it in 2D. So not only do numbers not randomly cluster in each row, but across each column and diagonal as well. Can this actually be done?