Colour correcting RGB LEDs - possibly with science
Well, the easy method would be to find a friend who can see colors and ask him to pick 16 colors for you. 

The first 8 colors (7 if you don't count black) are easy...just run through all the possible combinations of on/off LEDs. To get more than that, you'll need to vary the brightness of the individual colors. Generally you vary LED brightness not via voltage, but via PWM (very quickly turning the LED on and off. Spending more time off to make it appear dimemr)