The Gain of the Patch Antenna more than 8.2 dB

I simulated a patch antenna in HFSS. The simulated gain is more than 8.2 dB. Is my simulation reliable?
My solution frequency is 2.245 GHz, and my substrate is vacuum with a thickness of 5 mm. Any suggestions appreciated?
Thank you in advance!

For low dielectric constant material ( like a vacuum) you can get this much patch antenna gain. But you are taking vacuum as substrate, how you will realize this antenna in practical?

Thanks for your reply. I can use styrofoam as substrate since it's dielectric constant is close to that of vacuum. My simulated gain is around 9.4 dB, which is more that the maximum estimated gain 8.2 dB for a patch antenna. I tried refining the mesh but my gain is still more than 9 dB. Also one thing I noticed is that my antenna efficiency more than 1. how it is possible have an antenna with efficiency more than 1?!
Please share with me if you have any ideas.
Thanks!