RE: Savage 110 E. 30-06 What is a good round to use?
I agree with James B, concerning your checking for loose mounts and/or rings. Also of primary importance is to have the mounting bolts for the action torqued down tight. Loose screws/bolts are the main reason for too large groups. Certainly making sure that the bore has been cleaned out very well and free from copper fouling is important too. Some products like CR10, that can really cut copper fouling should be used. Be sure to not leave the bore dry if you are going to store the rifle and lube to prevent rust after cleaning with any strong product like CR10. Dry the bore with clean patches before taking two or three fouling shots, before again checking for tightness of groups.
Have to ask: If you test other rifles in the same manner, are you getting better groups with them? If not, are you resting the forestock on a pad that is not hard enough to cause the rifle to bounce upon firing. A hard surface against the forestock will open up groups. Then be certain not to rest the barrel on the pad, but rest the forestock on the pad. Same goes for the buttstock, which should be in a solid, padded "V" rest, in order to have the entire rifle stablized when firing for test, from the bench.