Delta 3200 with its comparatively strong grain is preferably used when it is dark, so the choice of developer should account for that:
- You are ready to accept some grain but want to shoot at high EI, which calls for developers which can reach the maximum emulsion speed of this film. Think Microphen and its home brew variant ID-68, Xtol/Mytol/Mark Overton's D316/Ryuji Suzuki's DS-10, there are also some Crawley formulas for achieving maximum emulsion speed.
- You could want to go beyond emulsion speed, i.e. push the hell out of it, grain be damned. Look for developers recommended for pushing, either the ones listed above, or, as I have been told but those more knowledgeable than me, D76 supposedly pushes better than any other dev. If you like to experiment, someone pushed Tri-X to EI 25600 with his "push soup". He uses a mix of proprietary developers, though, but only the HC-110 part is difficult to impossible to home brew for mortals, and chances are it could be replaced if one tries.
- Another issue with night shots is their extreme contrast. It's not only from light sources in your frame, and from lack of a highly diffused fill light source (aka the sky), you also have to account for reciprocity failure with long exposures. To deal with this I had some very nice results with Delta 3200 and ultra low contrast developers (think POTA). The Film Developing Cookbook has a nice chapter on these developers, highly recommended!