Does the term "transistor" mean anything to you? I've been inside many dot matrix printers, ranging from thermal to mechanical types, and none of them used relays. The reason is that relay timing is so imprecise and slow.

You can buy mosfets today that can easily handle multiple amperes ans switch them in a few microseconds or less. Bipolars don't do badly either. You can choose mosfets that can be driven directly from your MCU if you like, but with the number that you want, well, you may need external logic. If you look at the many threads that there have been regarding LED drivers, perhaps that will shed some light.

While the typical scanning column arrangement for your print wires will probably work, you may find that the approach some LED displays use may work just as well and can be applied to driving the "electromagnetic coil actuators" to which you refer. Relays are, after all, little else. Any thing that can drive a relay can drive what the relay drives if the voltage and current are reasonable. Most of the printers I've examined have used bipolar transistors rather than FET's to drive their impactors. I've seen character based dot-matrix printers that had shuttle mechanisms that moved multiple printheads a short distance rather than a single one a long distance. I've seen printers that had multiple columns of print needles, enabling them to print an entire character at a time, and, of those, some had multiple printheads. They've all given way to less massive mechanisms, though.

There are solid-state ways of doing what you probably have concluded you need relays to do. I think you're better off without them, as they just complicate your timing. Relays, generally speaking, operate in milliseconds, with a tolerance expressed in milliseconds. The ones that are fast can easily be replaced with solid state hardware costing less and capable of greater currents.

RE