One that can carry a reasonable number of high-performance aircraft.There is no way you can get a useable CATOBAR aircraft carrier under 40,000 tons.
Define "useable"
But again, I would have to ask "what is a reasonable number". For instance, I am sure that operators of the Centaur-class, Colossus class, Majestic class and Clemenceau-class aircraft carriers would have felt that their ships were useable and carried a reasonable number of aircraft in their time. Compared to other larger ships (especially US super carriers) they would have appeared small, unusable and not carrying a reasonable number of aircraft but it is all relative and different from the perspective of the operator. I am sure one could still develop a sub-40,000 tonne CATOBAR carrier today. Unless you put actual specs to something, just using subjective terms such as usable and/or reasonable is meaningless.