Its a 3" filter.
That is a small air filter and may be the reason you are needing to run small main jets. The jetting specs that most guys are giving your are based upon having the stock rubber boot between the carb and a much larger air filter. A LT 500 with anyones big or small filter clamped on the back of the carb, will not usually produce as much power as one with the properly designed intake system.
I would suggest that you get an air box or use the stock carb to air filter boot then maybe some of these jetting recommendations will work