The Pokémon Tretta Lab Main System utility has got various features which rely upon the data of the Pokémon Tretta pucks. Within the Type Checker, there is a list of all the Pokémon Tretta in each of the sets. However, the game initially only gives you a small list of multiple ones within each set. Each set is separated from the other to allow for easy scrolling.
As you scan various Tretta pucks, they will get added to the Tretta List. You can see which ones you own through a blue light to the side of them.
More sets and promos get added via the SpotPass Downloads