Hi tried to post a reply as in ronsimpson's post, but had some difficulty doing so. Here is my thoughts.
What I am sayings is if you want the power supply to supply a continuous 3A then the transformer needs to be rated at 3/.566. This figure came from two sources, 1 Triad Transformer Co. and 2 from a transformer manufacture friend of mine. As you know the peak voltage of the transformer is 1.414 times the rms. The filter capacitor will charge to near this value. Since the average load curreuld be 3A then the peak charge current is close the double that or 3/.566 so if the transformer is not rated at near 6A rms load current the winding supplying the current will heat up.
I am on a short vacation so I am away from home and don't have my notes with me so when I say the average value of a brute force filter capacitor is 3000uf per amp. I know there is a formula that has ripple voltage frequency and load current to calculate the exact value of capacitor required. I have built a great number of linear power supplies and have been real successful with the 3000uF/amp. I once built a high current linear power supply and the transformer was getting hot, so a did some research on max current.
Thanks you so much, really. You even replied when you are on a vacation. =)