Theres no exact size of a big firm. Also it depends on city, for eg in Pune 5 partner firm is a big one but in Mumbai the same will be one the small firm.
As you haven;t stated the name of the city where u wann pursue ur articleship, its difficult to give a precise answer. You can ask your seniors, they will be in a better position to tell you the same.
Try big4 and RSM, Batliboi, AFF, BMR, K&M etc
Also Firms of our past presidents of ICAI are also good.
I want to correct what Pritam has said. Batliboi is not a different one,it is EY itself. But after big 4 ,amongst top indian CA firm is NM Raiji along with AF Fergusons.Lodha doesnt exist any more now coz of their disputes ,all birla Cos are gone from them.