Controller info

For a better answer here, we would need to know what you are switching. What are the electrodes connected to, for example. (audio, high- voltge, sensor arrays, digital data)/??

An obvious solution is to use relays, and employ a bunch of latches under microprocessor or microcontroller control. But like I said, depending on what you want to switch (control), there could be much easier, and less costly ways to get there. -mpm

Are you concerned with controlling a digital logic state, an analog voltage into a high impedance, or into a low impedance, or are these 'electrodes' parts of a phased-array antenna, each with a target phase-shift and amplitude?

There are multimillion-electrode storage electron tubes in the literature, and it would be trivial to scale down to 20 x 20. Microprocessor output for this would be a video card... There are test equipment designs for LSI production lines that have 'pin drive' heads that would easily do 400 pins.