Based on the network bands it can use, I would say that it is the T999
, because it's not said the phone can access LTE on 700/1700/2100 MHz. (Unlike, for example, the Sony Experia T: in its page, it is explicitly written the Experia T can access LTE on those bands. There is no precision for the Samsung Galaxy SIII, so I would think the phone model is T999.)
But you can confirm with Eastlink support to make sure this is the correct phone model.