I am renovating the rec room in my basement. The heating system is forced air. Currently, the warm air in the basement is distributed through ducts in the floor joists above. The warm air outlets are in the ceiling of the rec room, so the air blows down into the room. On the first and second floors of the house the warm air comes into each room from floor level inlets, placed for the most part below a window.
Is there a technical reason the air inlets were placed in the basement ceiling, or is this something the contractor did to save the effort of running ducts down the walls of the rooms in the basement?
Should I run ducts down the walls and have the warm air enter the room close to floor level?

It will make for a warmer basement if ran down the wall channels. Especially the floor. Our company always stresses the importance of blowing the air across the floor. As for the original installation I'm sure it was the way that contractor or builder was used to doing and of course the extra $ & cents.
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Thanks for your help.
Will the amount of air coming through the duct be reduced when I lower the outlet to floor level? At this point the outlet of the duct will be about 7 feet below the plenum.

Also, the most convenient place to let the warm air into the rec room at floor level, is close to the return air duct, which is also just above the floor. If the inlet warm air duct and the colder return air duct are on the same wall, how far apart should they be?

It is very important to add return air ducts to your basement to insure humidity and heat don't build up. You can tee into your existing return and run a vent down to 6 in off the floor. This will level out your basement temps even more than lower the supply ducts.