Per a few members' suggestions, so that all R8 info is on the same thread, I am adding in this thread something I posted a few months ago in another thread in response to a member's question 
R8 scope mounts clearance
Based on factual experience with 8 different barrel / scope R8 combinations, I had to actually exchange 2 "low" 30 mm scope mounts for 2 "high" 30 mm scope mounts.
There is a potential clearance issue with the Blaser scope mounts, but contrarily to the classic issue of front bell clearance, with the Blaser mounts, the issue is with the turrets housing bottom.
About any reasonable objective diameter I can think of, including 56 mm, will easily clear the barrel (and the rear sights if present) with a low mount, whether 1" or 30 mm.
What may not clear, is the bottom of the turrets housing...
Let me explain and illustrate using six examples...
Here is a Swarovski Z3 4-12x50 in 1 inch high mount on a standard .223 barrel. Observe how the 50 mm objective comfortably clears the barrel. This was my first Blaser mount, and I used a high mount because, like you, I did not know - and could not find out - if a 50 mm objective would clear a low mount. Turns out it would clear it easily.
Here is a Leica Magnus 1-6.3x24i in 30 mm low mount on a Selous .458 Lott barrel. Observe how, of course, the straight tube clearance is indeed not a concern, but observe also how little clearance the low mount leaves to the bottom of the turrets housing. There is not much margin, and it works ... but just barely...
Here is a Leica ERi 2.5-10x42 in 30 mm low mount on a semi-weight .375 H&H barrel. Observe how the 42 mm objective clearance is also not a concern, but observe also again how little clearance the low mount leaves to the bottom of the turrets housing. There is not much margin either, and it too works ... but again just barely...
Here is a Zeiss V4 4-16x50 in 30 mm low mount on standard .300 Wby barrel. Although there was plenty of clearance for the objective bell,
observe how the bottom of the turrets housing is bottoming out. I immediately saw this but still tried against all visual indications.
When I tightened either front or rear ring, the scope tilted front or back, clearly confirming that the low rings are lower than the turrets housing bottom. I had to return and exchange two low 30 mm scope mounts for 2 high scope mounts...
Here is another Zeiss V4 4-16x50, this time in 30 mm high mounts on a standard .257 Wby barrel. This is one of the two scopes for which I had to return and exchange a low mount for a high mount. Observe how the clearance for the 50 mm objective is largely superior to the clearance for the bottom of the turrets housing.
Here is a Zeiss V4 4-16x44 in 30 mm high mounts on a standard .270 Win barrel. Observe how the clearance for the 44 mm objective is disproportionate, and would be easily accommodated by a low mount, but how the clearance for the bottom of the turrets housing is still what mandates a high mount.
Observe also how in all cases, the scopes easily clear the rear iron sights, not visible on all pictures, but present on all barrels, because Blaser install the rear sights way forward.
In summary, yes, there are some mount height limitations for the R8 with the low mounts either 1" or 30 mm, but in my experience the diameter of the objective bell is not the limiting factor (at least for common sizes, up to and including 56 mm). Check carefully the bulging of the bottom of the turrets housing...
I hope this helps
