The article on DBSCAN "https://www.aaai.org/Papers/KDD/1996/KDD96-037.pdf" explains that the minpts value must be 4 for any datasets on which the DBSCAN is being used for clustering the data points. Does it gives the best results for any Eps value??
In later work, the authors suggest to use minPts = 2 * dim as default.
J. Sander, M. Ester, H.-P. Kriegel, and X. Xu. 1998.
Density-Based Clustering in Spatial Databases:
The Algorithm GDBSCAN and its Applications.
Data Mining and Knowledge Discovery 2, 2 (1998), 169–194.
http://dx.doi.org/10.1023/A:1009745219419
If you have duplicates, use a larger value: "Our experiments indicate that this value works well for databases D where each point occurs only once, i.e., if D is really a set of points."
Smaller values are usually more computationally efficient. Thus, keep minPts small but not too small.
Always study your result. Never use it without double checking.