This along with the convexHull3D from wouter fixed the problem. The solutions we tested were 3 percent better than the approximation we were using, we will probably switch to that method. From the remaining circles take the one with the minimal radius. This algorithm guarantees to give the correct result.
Warnings arise from identical points or three points on one line.
However, these warnings can be ignored. From the remaining spheres take the one with the minimal radius. Checks of the result can be done as above. Therefore, this algorithm has probably no real world applications.