Is it possible to get an exponential capacitance curve from coded dip switch
Edited: 

The 4 relay idea from Tom C is one option.  

Other then that, if using a group of relays is not practical, then an old fashion 16 position rotary switch could do the trick too.  

You could create a similar capacitor string as in your first diagram using 16 equal value capacitors, (much easier then finding several specific values) then use the 16 position switch to connect to each of the 16 intersections within the string.  That would give you the "division" format you seem to need. 

Low cost 12 position switches can be had from surplus dealers.