The Bulgarian scientists frequently estimate the egg laying rates (as part of the breeding program).
The they use method which includes 24 h confinement of the queen to a single frame using 2QX (i can't remember the name of the device right now), then the eggs are counted. This procedure is repeated every few days or so and then at the end of the month is calculated the average rate for that month.
The actual brood area is more important factor to me. It doesn't matter really how fast car you drive when there is a speed limit.
According to the Bulgarian scientists the most fertile queens lay up to 3600 eggs per day (average), which is very ordinary queen to my understandings. Double that figuire is more close to the absolute maxumum (I almost can hear you laughing). Just because you can't lift 200 kg weight, it doesn't mean that there are not people who can't lift 500kg (Steve Goggins, Mike Millers, Andy Bolton... and many others).
It's not important how many eggs a queen can lay. It's much more important how much honey you will get. More eggs means only that you get more brood, not necessarily more bees and more bees not always mean more honey. With increasing fertility usually you get shorter lived bees. So you must find a balance between fertility and longevity, if you want more bees.
Also, is more important that the bee fits for the hive you're using, or you have to change something. You cannot expect any success by keeping prolific bee in a too small hive, or moderately fertile bee in a capacious hive.
The different strains of bees differ considerably in fertility.
