My name tells you why I know this.
Back in the day when there were more airports, fewer planes, and fewer VOR (and paired DME) frequencies, a range limit was needed to keep from locking on to the wrong DME station. Standard was 70 miles for ILS and LVOR-paired frequencies, and 200 nmi for HVOR-paired.
LVOR is/was a VOR for low altitude navigation.
DME is in the 1GHz frequency band, so range is definitely Line of Sight. Line of sight is limited due to earth curvature, of course, and in miles is 1.23 times the square root of the altitude in feet. Hence, line of sight at 10,000 feet is 123 miles, and at 40,000 feet it's 246 miles.
Line of sight is increased if the ground station is on a mountain top, such as Santa Barbara, KSBA, in California. It's at 4,000 feet elevation with a clear shot over the Pacific ocean to the southwest, so you can add about 60 miles to the range based on own altitude. If you get longer range than that, it's due to tunneling effect in certain atmospheric conditions, usually an inversion, and usually transitory.
You can see also my post #800(?) on the Brasil midair for more on DME and transponders.
GB