maximun gain achievable with dipole

i am modeling a half wavelength dipole parallel to ground plane in cst .
i want to see the effect on the performance of dipole with changing the height of the dipole above the ground plane.
when i look at the farfield pattern it is showing the gain apprx 8db which i cant explain.
the gain of dipole in free space is approx 2.14 dbi.
so when we use ground plane all the radiation is in the upper hemisphere so there will be increase in gain by 3 db so total gain should be 5.14dbi approx.
but i dont know why cst is showing 8 dbi for a dipole at the height of lambda by 4 from the ground plane .
can any one comment on this.

thanks

I wonder if you have accidentally simulated a full wave dipole? Corner reflectors can achieve much higher gains than flat reflectors. Do you somehow have a corner in the simulation?

Just a couple of things to check.

Kraus, "Antennas", sections 11 and 12 discuss this question. I'll leave you the fun of teasing the answer out of what he says. You might want to look at figure 12-9 for a 180 degree reflector. It seems to imply a 5 dB increase over a dipole which is almost the 8 dBi reported by your simulation. Thinking of this as an endfire array with two elements the result might just be correct

I have another fish to fry at the moment, so good luck. Let me know what you conclude.