Nitro Ammunition Company has a great website with a lot of advice on patterning and ammo recommendations. They helped me a lot with my turkey gun years ago.
One take-away was that for a lot of guns/chokes, a triplex type load (3 different shot sizes) helps the shot to "organize" better when it goes down the barrel so it holds it's pattern better. If you try to jam too much (or too large) of shot thru the choke, it can be counterproductive to retaining a tight pattern down range.
A harder material that the shot is made of is better than soft lead. Lead gets deformed as it travels thru the barrel and creates little flat spots which won't fly as straight. They "wander" out of the pattern.
Nitro Company Ammunition manufactures superior shotgun shells for 10ga., 12ga., 20ga., 16ga., 28ga., and .410ga. Our advanced technology using high quality components create dense patterns at longer ranges. Recommendations given on guns, chokes, and loads, depend on your hunting situation.
nitrocompany.com