I'm replacing an old basement floor drain that neither has a trap or a vent. The drain is in the lowest spot in the basement and is required for the occasional foundation leak. The new drain will be inspected. I've read quite a bit on this forum about the necessity for a trap primer and I have bought a PPP priming adapter to go above the trap and a ProFlo PFP 2500 valve (I've seen other brands recommended here, but this is what Ferguson had on hand.)

I'll be replacing the whole drain to where it intersects with an existing updated main drain, and adding a basement sink and new vent at the sink. The new sink drain will intersect with the new floor drain 16' away from the floor drain. The Oregon Plumbing Code section 1006.0 states that no venting is required for 6' for a 2" floor drain, but it looks like some sort of venting is required.

Can I run a horizontal vent to the nearest wall which is 3' behind the drain? (3' in the opposite direction of the drain slope.)

Thanks for any advice.