Hi:

Our house was built with roughed in plumbing for basement bathroom. I have the main drain pipe for the toilet protruding from the floor and what I believe to be a vent pipe just behind it in the middle of a studded wall also coming out from the floor. Within a few feet I have the main pipes that connect to the sewer lines. It would appear that the plumber did not allow for drain pipe for a bathroom sink. The plumber did allow for access to the main venting pipe of the house. Can I connect the sink drain to the vent pipe on the floor at the lowest point and above that point connect to the main vent pipe?

Come 18" off the floor to the center of a 2" sanitary tee in the vent to pick up the lavatory. The vent can continue on to revent back into a DRY VENT.
If you arm out with 2" you may extend the arm 5'. If you reduce to 1 1/2" you may only arm out 3 1/2'. Good luck, Tom