Generating non-colliding random numbers from the combination of 2 numbers in a set?
<p>I have a set of 64-bit unsigned integers with length >= 2. I pick 2 random integers, <code>a</code>, <code>b</code> from that set. I apply a deterministic operation to combine <code>a</code> and <code>b</code> into different 64-bit unsigned integers, <code>c_1</code>, <code>c_2</code>, <code>c_3</code>, etc. I add those <code>c_ns</code> to the set. I repeat that process.</p>

<p>What procedure can I use to guarantee that <code>c</code> will practically never collide with an existing bitstring on the set, even after millions of steps?</p>