optimum number of elements used in smart antenna

I am trying to get the idea about the optimum number of elements suitable for designing a smart antenna system. Is there any formula available for calculating the same?

I don't think so and I think the question is very odd to answer.
You need to design a particular Smart Antenna System based on the Beamforming requirements and interference cancellation needed and this is hard to define in a formula.
Why don't you check comsoc.org DL section for more information.

thank u for ur suggestion