Extending Tables

If |U| fits on a computer (as it does for Rhode Island license plates, or Duke student ID numbers), we're golden.

But what if n is small enough to fit, but |U| is large? For example, let's consider Duke student names:

• U is the set of all possible names, so |U| = 10²² (this is a conservative estimate based on 16-letter names).
• n is around 10,000 total students.
• We can store a table of around m=500,000 with no difficulty.
• This would make $\alpha = n/m = 0.02 < 1$.