I hadn't read everything yet but I went ahead and posted one of the largest I've seen recently. I didn't realize it was a competition though.
If the "bigness" is solely size, one could create a very large 2-color (BW) image that would take up very little memory, in comparison. Alternatively, a 1x1 GIF could have a huge memory footprint, although the degree of information conveyed to a human would be extremely minor in such an image.
4chan has a High-Res board, but it's NSFW in many cases.