So, I think I discovered something in Super Training.

After around 4 hours of the game software being fully closed, your pokemon have a chance of becoming fully rested.

Once fully rested they will appear to be lying down flat. When clicked on they have a (...) bubble over their head. When you touch them it will let you know that they are rested, however, sometimes they will gain a happy ecstatic bouncing mood with a [ :D ] over their head.

I found that training on the blank bag when they are like this results in a very large amount of L and M bags (of all kinds).

I have tested this several times and believe it to be solid.

Sorry for the bad quality. Pic is of my Leufeo with the [ :D ] ecstatic mood. About to post results.