Air drying your laundry keeps it nicer anyway, but this is especially true of whites, in my experience. Treat them for stains (vinegar or a baking soda paste [but never both at once, lol] peroxide, oxygen bleach [not chlorine bleach, that stuff eats fabric]), wash, and line-dry in the sun. The sun will help keep your whites white.
The trick I use, that works wonders, is washing soda. Looks like baking soda, made by arm-and hammer, but don't try baking cupcakes with it. Boil your whites in a pot on the stove, wring 'em out when they cool enough to handle, and line dry them. Pearly white. I use it for my binder and undershirts, which get deodorant stains on them alot recently.
You can also take a trick from the laundry detergent manufacturers and use a teensy amount of blue dye in your whites load, to make them look bright (that's how 'optical brighteners' work) but try this at your own risk. I only mention it for educational purpose.