Transistor resistance for switching analog signals
For 16-bit performance you should use a high quality analog switch such as an ADG511, and buffer the output of the multiplexer with a precision op-amp that has low bias current (and offset voltage, and high open-loop gain). The analog switch includes low leakage, low Rds(on) switches and level shifting from logic. 

Back in the dark ages, it was sometimes done to use bipolar transistors with controlled currents to the bases to switch precision analog signals (symmetrical transistors have very low Vce(on) under just the right conditions) but you do not want to do that. See for example this 1961 (!) reference, if you're interesting in paleolithic circuit design.