control 250 doors with arduino

As usual, there are a number of ways to do this type of thing.

Perhaps take a look at this tutorial using daisy-chained shift registers:

https://www.arduino.cc/en/Tutorial/ShiftOut

You could use 5x Arduino Mega256 microcontrollers which have significantly more digital IO than an UNO . This may seem ridiculous but could work out easier/cheaper.

Another approach is to move some of the 'intelligence' closer to the locks and use a bus type approach where each lock is given a unique address on the bus and only responds to bus commands with that particular address.

Dave's last suggestion seems to be the most practical one, if you don't want a wire bundle as thick as a tree's branch.

That would perhaps depend on where you located the shift registers though. If the lockers are arranged in an XY matrix then you could perhaps space the shift registers at 8-locker intervals along the 'X axis' reducing the wire bundle at any one location considerably.

Same with the distributed microcontroller approach - each ATMega328 microcontroller could service around 20 lockers with digital IO and then use a communications bus between them along the 'X axis'.

Adding the intelligence at each lock may be costly as you have the 250x factor to consider.

A mix-and match approach may be reasonable for both costs and wiring.

addressable bus devices with enough pins to control a set of doors, placed localy close to these doors. And then a bus line linking all of the bus devices together and to the arduino.

You'd also have to run a power line and some devices that can switch significant current, because locks are most of the time actuator-controlled. This device can be a relais or an electronic switch.

Because the actuators will generate significant pulses, your bus line has to be resiliant for that. dough suggested a line that can bridge some distance and is relatively forgiving for pulses.

I would't bet on SPI or I2C. They both do well on a pcb, but when you use them with lines of some distance, with 250 possible sources for magnetic pulses (500 sources if the locks are controlled by a relais), chances are dim that it 'll work reliably.

A mix-and match approach may be reasonable for both costs and wiring.

addressable bus devices with enough pins to control a set of doors, placed localy close to these doors. And then a bus line linking all of the bus devices together and to the arduino.

You'd also have to run a power line and some devices that can switch significant current, because locks are most of the time actuator-controlled. This device can be a relais or an electronic switch.

Because the actuators will generate significant pulses, your bus line has to be resiliant for that. dough suggested a line that can bridge some distance and is relatively forgiving for pulses.

I would't bet on SPI or I2C. They both do well on a pcb, but when you use them with lines of some distance, with 250 possible sources for magnetic pulses (500 sources if the locks are controlled by a relais), chances are dim that it 'll work reliably.

... If you route unadressed 'raw' control lines from the arduino, any hacker can get access to all sporter's wallets and iPhones with just two needles and 1 or 2 coin cells. With that, you can put a pulse on every line and see the lockers jump open one by one.