How far is VATS range?

This is related to my other question regarding weapon distance.

Often, I can see enemies but can't initiate VATS until I get closer. Exactly how far is this limit?

Do my stats (like perception) affect this in any way?

From what I've established (although I could probably do a little more research), there are three distinct ranges that enemies can come under:

Out-of-sight

This is pretty self-explanatory. The enemy is too far away to see, they have not yet rendered on the screen as they are simply too far away. There's not much that you can do about this, except get closer.

In-range

Again, pretty obvious. An enemy is within range of your weapon, and you can target them with VATS. Your percentage chance to hit in VATS will depend on the range/accuracy of your weapon, your level of perception, your perks and your distance from/ vision of the enemy.

In-sight, Out-of-range

This is the most interesting range. I've been too far away from an enemy to use VATS, and it would not initiate the VATS screen. However, using a sniper rifle (with a medium scope), I was actually able to hit it. Despite having 0% chance to hit in VATS, I was still able to do damage from that distance.

I'm guessing the weapon 'range' stat had something to do with this, and shooting a weapon (even accurately) such as a 10mm pistol or shotgun would not have done damage. I had a modified hunting rifle with the range stat maxed as much as possible for my level (which was ~220, just for reference).

To know you are within the in-sight, out-of-range distance is simple. Usually when you press the VATS button there is a 'click' that accompanies it when there are no enemies (or allies) within your field of vision. However, if you click to enter VATS and it does not make the clicking noise, but still does not enter VATS, then you know that there is an enemy within your field of vision, and in-sight, but out of range for VATS targeting.

They will usually still be difficult to spot manually, as they will be at a great distance, but can still be hit if they are within range of your weapon. I'm not 100% on whether the click for failing to enter VATS occurs when an enemy is in the field of vision but obscured (behind brush or a tree for example). However I'm quite sure that the VATS screen is only initiated with an enemy in your line-of-sight if there is a greater than 0% chance to hit any body part (with a ranged weapon anyway, melee will still show 0% chance to hit (Thanks to DCShannon for clarifying this)).

I also haven't done any experimenting with the penetrator perk, as this may affect whether the click occurs when an enemy is obscured but within range.