Our pupil's maximum dilation is 7 mm. That means, an exit pupil for maximum light needs to be 7 mm. After that, it's a compromise you have to make regarding how much magnification you can handle/use, and how big a front objective you can tolerate in mounting.
exit pupil x magnification = max objective diameter in mm
7 mm x 4x = 28 mm (note: 1 inch=~25 mm)
7 mm x 6x = 42 mm
7 mm x 7x = 49 mm
7 mm x 8x = 56 mm
7 mm x 10x = 77 mm
physics rule:
"The intensity of light varies inversely to the square of the distance from the source."
Bob Bell wrote an excellent article in the 1989 Gun Digest (43rd edition, red cover, page 6) called "Why big scopes make a difference." It addresses why "big" scopes are brighter in darker conditions.
If you have a target at 500 yards away in dark or twilight conditions, you may just be able to make out the object. If you have a 6x42mm scope mounted (a pretty good practical low light scope due to the 7 mm exit pupil it gives and relatively low scope mounting), the effective distance through the scope is 500 yards/6x = 83 yards. Square the number (83x83) to get a value of ~6890. The inverse is 1/6890.
This means the light intensity reflected from the target (visible to the eye) is 1/6890 of what it would be at 1 yard. You would see the object at 1 yard, but the further away it is, it gets harder to see.
Compare the same object (same dark conditions and 500 yard distance) with two other "big" scopes".
An 8x56 scope would give an effective distance of 500/8 = 62.5 yards. Square this (62.5 x 62.5)to get a value of ~ 3900. Take the inverse, and you get 1/3900.
A 10x77 mm scope would have an effective distance of 500/10 = 50 yards. Squaring this yields 2500. The inverse value is 1/2500.
This means the light intensity of a 10x77 scope is 6890/2500 times more "bright" than the 6x42 scope, or 2.7+ times brighter. (6890/2500 =2.756)
Compare that to a 4x32 scope. The 500 yard target has an effective distance of 500/4=125 yards. Square that to get 15,625. The light intensity reflecting off the target is the inverse of the square, so the reading is 1/15,625 or, 2500/15,625 times LESS bright ("intense") for a value of 16% of the intensity ("brightness") of the object seen through a 10x77 scope.
How about that 2.5x scope that was marketed to have a high "twilight factor" due to a "large field of view." Same object/distance/light conditions gives you an effective distance of 500/2.5 = 200. Square this to get 40,000. The inverse of the squard is 1/40,000 or 2500/40,000 = 6.25% of the light intensity compared to the object seen through the 10x77 scope at the same distance and conditions.
It's not just magnification, it is exit pupil, or the "tube of light image" that gets to your eye's maximum "open iris condition" of 7 mm, which exits the rear objective of the scope into your eye. That's the rate limiting reaction on the receiving end-7 mm exit pupil.
You then have all the mechanical issues with quality of the glass and lens coatings for light transmission. You the have to make the decision of how big a scope you want on your rifle (how high to mount it). An 8x56mm scope has a front objective bell diameter over 2 inches wide (56 mm/25.4 mm per inch = 2.2 inches). A 10x77mm scope would have a 3 inch front objective diameter.
What's the BRIGHTEST scope? It's the scope with the highest magnification you can use, with the largest mountable front objective you can secure, that gives you a 7 mm exit pupil, that you can tolerate or use for your hunting conditions.
That's the physics behind it. The rest is up to you, and your wallet. Try to find Bob Bell's article. It is a classic.
