Solving the NFS 16-Group Limit Problem

I apologize for the verbose post. This is a complicated problem and it merits full¬†explanation. If you are experiencing this problem I advise you to avoid skimming and read it very carefully :) Sometimes you come across a problem that is a little more complex than average. Sometimes it is problem that is rare enough that there isn’t an obvious answer in the first google hint. Sometimes a problem may seem unavoidable, which leads to work-arounds, and before you know it you have a mess.