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LDC1612: Advice for maximising measurement distance

Part Number: LDC1612

I wish to design an inductive sensing system and the main aim is to maximise sensing distance, accuracy and resolution is not so important, can be around 1mm or less.

From my I understand so far:

Use device with high resolution e.g 28bit L measurement.

Use largest sensor diameter (in my case probably 48mm or higher if possible).

Use maximum frequency e.g. 40MHz.

Here are my questions:

1)      Is there any benefit if the target diameter is greater than the sensor diameter e.g. x1.5, x2.0?

2)      Does it improve measurement distance if the target material is more magnetic (higher magnetic permeability) e.g. 430 grade magnetic steel?

3)      I have read that placing a ferrite directly behind the sensor coil (opposite side to sensing direction) will increase the inductance of the sensor coil and this increase measurement distance. How exactly is this meant to be implemented, I see two options, insert a ferrite disk inside the ID of the sensor coil through a hole in PCB, or fix a planer disk of ferrite behind the sensor coil PCB which covers the whole OD? Does this need to be a high grade ferrite material or would lower cost material such as Iron, Mild steel or magnetic steel also provide benefit, or is it a case of higher magnetic permeability means higher sensor coil inductance, so a cost / benefit trade off?

Many thanks