2⁴⁰ is about 10¹² entries, so if you're unlucky, you may moving into the territory of very large databases (see, for example, this site).

It may help if you give a description of what sort of problem this is intended to solve. Somebody here may have a better algorithm. Of course, if you've already got the optimal solution, you may want to write it up in a paper to present at one of the upcoming VLDB conferences.