1. A Sampling Problem for PerfectClub Convex Hull Database:

An interesting remark on the results regarding our sampling implementation is that, in this unique case, we have a small incoherence in conclusion for the PerfectClub sampled database and its full database: 6_fig:PerfectClub_convex_hull_dimension_C3C64_C3P64_100 shows that C3C64 is about $3$ times faster than C3P64, concerning the total run time. It is in fact the contrary to the result obtained with the full database.

This means, in our sampling of interval $100$ on the PerfectClub convex hull database, where we randomly take $1$ test from every 100 tests, a few tests that are not suitable for the partial factorization have been eliminated. We have not investigated this problem yet.

Figure 39: PerfectClub: Dimension C3C64 vs C3P64 in sampled database - too few tests

Our conclusion for timing performance of these two algorithms is that C3C64 is faster than C3P64, with the convex hull full databases.