I need to make a random list of permutations. The elements can be anything but assume that they are the integers 0 through x-1. I want to make y lists, each containing z elements. The rules are that no list may contain the same element twice and that over all the lists, the number of times each elements is used is the same (or as close as possible). For instance, if my elements are 0,1,2,3, y is 6, and z is 2, then one possible solution is:

0,3
1,2
3,0
2,1
0,1
2,3

Each row has only unique elements and no element has been used more than 3 times. If y were 7, then 2 elements would be used 4 times, the rest 3.