Hi Dennis,
One thing that is needed is to know is on which PI the coil is going to be used. This makes a big difference. Also, there are already some PI's that have large coils already built for them so it might be possible to purchase one already built.
As for building one yourself, I have never seen specific instructions on how to build a particular coil that seems to work for all conditions. So, I will try to give a generic answer to your question about possibly building a coil to cover or scan a 3 foot area.
First, either a DD or a mono coil can be built to scan the area you mentioned. The coil could be built in several shapes such as a rectangular, an elliptical, a round coil or some other shape to fit the specific need.
The object of building such a coil to fit a certain detector is to best duplicate the characteristics of the coil already used on that particular detector. In other words, one should try to match the inductance and resistance if possible. The coil cable should be matched also.
By doing this, the new coil will appear the same as the original coil, thus the damping will be correct which will allow all to work correctly. If there is a distinct difference, then it is quite possible the coil will not work correctly or not at all.
Unfortunately, I have not tried to build a coil the size your desire so I have no actual experience. However, I have built different sized coils and there is subtle differences between them. My guess is in building a larger coil the size you desire, you will still have to match the original smaller coil as close as possible. However, this is difficult because of the additional capacitance as the result of the larger windings, etc. So, it might need some changes to work correctly.
Other factors have to be taken into account such as the Faraday shielding and the selection of the coil cable. Both are critical and can have a significant influence on the final success or failure of the design and its intended use.
Generally speaking, larger coils are more difficult to build and still allow very short delays. On some detectors such as the Goldquest, or one of Eric's other detectors, the detector design is very forgiving meaning they seem to work without trying to maintain absolute tolerances.
Again, it may not be possible to get the coil to work at the short delays a smaller coil might be able to operate at but may work fine when the delay is advanced.
Ideally, one should have an oscilloscope to observe the signals of the new coil. This will allow you to see what is really going on and if the coil is properly damped or not. If the damping is incorrect, the coil may oscillate briefly which will cause problems until the oscillation subsides. Overdamping may cause the detector to fail to work until the delay is advanced.
Now, I really not given you a specific answer to your question but I have tried to at least point out some of the problems you might encounter.
Personally, I built several coils with different inductances and tried different shielding before I settled on my present designs. Part of the reason for this was I was trying to find the right combination that would allow for a shorter delay than the detector was originally designed to operate at.
If I were to build a larger coil the size you desired, I would expect I would have to do the same once again. I would still try to match my present inductance as much as possible and would continue to search for the ideal coil cable to minimize the capacitance. My guess is I would have a very difficult time trying to get a coil as large as you desire to operate at the same minimum delay I can operate smaller coils.
I hope this helps somewhat and at least gets you started.
Reg