Which rifle and which type of Talley rings?

The 4-16x44mm VV HS has a bell diameter of 2.03” and a 30mm tube, which means it needs 1.02” minimum ring height (bottom to centerline) to set on top of a flattop - plus .125” desired clearance, for a total height above receiver of 1.145”. But... If you have a sporterweight barrel which droops in front of the chamber by 1/8” where the objective taper would touch and two piece bases which sit 1/4” above the receiver, you might get away with less than 1.0” rings (aka lows). If you’re talking about integral bases and a bull barrel, you might need the full 1.145”.

Easy solution, if you have the rifle and optic in hand - cut a deck of playing cards into two sets of 1/2” wide strips. Set the rifle in a vise, make two even stacks of card shims about 1/2” tall, set them on the receiver, and then set the scope on the shim stacks. Add or remove shims from each stack to create your desired clearance out front, measure the stack, add 15mm for the tube diameter, then buy that height of rings.

I have “Low” rings on my match rifle - a Heavy Palma barrel and Bushnell DMR II 50mm objective. Nothin’ but a name, the dimension is what makes the difference.

The Talley integral base rings for the Rem 700 are .43” for the Lows and .53” for the Mediums, from receiver to bottom of scope tube. As noted above, the center of the tube should be 1.145” above the receiver to give 1/8” clearance. The scope tube on your Vortex is 30mm, which is 1.18”, half of which is 0.59”. For our ring height: 1.145” - 0.59” = 0.55”.

Considering the Rem 700 action is 1.35” diameter, and typically have 1.20” or 1.25” barrels, we pick up 0.05-0.075” of clearance. 0.55-0.05” = 0.50”... so Mediums would work. Low’s would FIT, but would only allow approximately 30thou of clearance, not the 1/8” clearance we want.

So looking at the specs, Mediums are your huckleberry.