This article: https://www.instructables.com/id/Simple-Arduino-Metal-Detector/
Was the original inspiration, and we mostly stayed true to the circuit shown, besides making the circuit switched using a FET, rather than sourcing current from the microcontroller, and adding a flyback diode for protection.
(The article has a great explanation on the workings too)
For the first prototype, we decided to simply wing it when it came to dimensions, coil turns etc. by making the board the size we wanted it to be and seeing if we could make it work.
Surprisingly, it worked out quite well!
(please excuse the vertical video..)
We are currently testing 6 layer versions of the board in an attempt to increase the resolution on the sensor.
Very cool and nicely executed. Wondering if it can potentially work well with lead pencil or else conductive silver ink pen. That would make it more convenient to draw a maze or what have you.