How do I connect 200 LEDs to arduino?

Other Hardware LEDs and Multiplexing
4

With 200 LEDs only taking 500mA that only leaves 2.5mA per LED.
They are not going to be very bright at that.
You can wire several in seriese, at 18V you could put 9 LEDs in seriese, and boost the current to 20mA through the LEDs, is that what you want to do?