Some properties of Cartesian product files

In this paper, we first introduced the concept of Cartesian product files. We then derived a formula for random files. A computer simulation experiment was performed to compare these two files. So far as shown by the experimental results, the Cartesian product file concept was indeed a good one. We also showed that the problem of designing an optimal Cartesian product file was partially related to the problem of finding a minimal N-tuple. A method to find minimal N-tuples was presented and its properties were discussed.