What gain antenna is required to achieve the stated range?

I want to use XBee S2C DigiMesh 2.4 through-hole module w/ RPSMA connector XB24CDMSIT-001 with a whip antenna. I can get antennas with gain ranging from 2dBi to 9dBi.

What is the minimum gain required to achieve the specified Xbee range?
What is the maximum gain permitted to keep within regulatory limits in Europe, USA?

The standard indoor/urban range was achieved using a 2.1dB gain antenna.

Outdoor Max RF LOS range is achieved with the max antenna gain allowed in the U.S. and listed in the manual with required cable loss.

EU only allows for a 2.1dB gain antenna.

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I am looking at page 144+ in the Digimesh Dev Kit User Guide.
The devices passed certification with omni-directional antennas:
EU 15dbi @ 10dBm
FCC 9.3dB, no cable loss

So although the range might be based on a 2.1dBi antenna, the rules allow for a lot higher gain

For the EU, to quote this site:

…In Europe at 2.4GHz we are limited by ETSI regulations to 20dbmW.

That is 20dB gain above 1mW or 100mW Effective radiated power compared to an isotropic (0 gain) aerial. This figure includes the gain from the aerial and losses from cabling.

So to calculate the EIRP of your system:
EIRP=Output power of card or access point in dBm – cable loss in dB – connector losses in dB + aerial gain in dBi

A typical card gives out +15dBmW so the largest aerial allowed is +5dB. However on a typical installation an +8dB aerial can be used as there is quite often a 3dB loss on the aerial cable.

The exception to the above is France, where the maximum output power is limited to 7dBm (5mW EIRP) at 2.4GHz. …

So for a Digimesh @10dbm, that should allow for a 10dBi antenna. The Digi manual says 9.3dBi so that is consistent. Same for the FCC.

So a more helpful answer would have been that the specified range of Digimesh modules is based on a 2.1dBi antenna.
The maximum antenna gain (zero cable loss) permitted in EU, Canada, USA and most countries is 9.3dBi.

That should allow for significant improvements in line-of-sight ranges.