White is a perception. It can't be objectively defined.
In painting we got lead white (or flake white), titanium white, chalk white, and a plethora of others. (In general, titanium white will look 'whiter' than other pigments.) Something which looks white can look gray or tinted next to some other white, and a tint will look white next to a darker shade or color with more hue.
One might say the ultimate white is intense enough ight that it completely overloads the eye -- for a moment, until you go blind from it -- but that's not a useful definition. Maybe the closest we can come is fresh snow in bright sunlight since it's harder to find anything which looks whiter in comparison, but it's more useful to say 'this' looks whiter than 'that' in a direct comparison -- but I expect that can vary depending on the individuals eyes and perception too.
White as a pigment will depend not only on the pigment but the light which is illuminating it -- and that holds for any other color as well. If you want to paint something that will render the colors as you want than you have to use the same light source as will be used by the person observing it, both in terms of spectrum and intensity.
If you want a diversion for a few years look up 'color theory' and note all the different schemes for trying to describe color.
http://en.wikipedia.org/wiki/Color for instance, as a start. The bottom line is that vision is not objective, and takes place in the brain and mind, and is relative to what else we see or imagine, and as filtered by the eye and nervous system. We might even see things differently depending on what we are hearing or otherwise sensing (see synesthesia). We can't say what IS white, only what LOOKS white, at a given time.