What you will need for "lowest" possible will have a lot to do with the scope that you chose - front end outside diameter - is some disagreement, but need perhaps more than sheet of paper clearance front end to barrel - is likely about thickness of a dime might be okay. Then scopes have varying diameters of eye bells - and some have big knobby things to give better grip to adjust power - can become a point of contact for the bolt handle. "Lowest possible" is likely like with a straight tube K3 Weaver or similar - many modern scopes have larger diameter eye bells - at the point of contact from bolt handle - and often shooters want more magnification than 3 power ...