Here's a reduced example. I want to ask whether an incoming 16 bit number is in my set. I can make a bitmap that answers that question perfectly in 8KB :)

So I'm assuming what the parent meant by sparse is, things where the universe is much much bigger, and therefore the things in your set are a sparse proportion of the universe. For instance, in deduplication, we use at least 160 bit hash functions...and that bitmap isn't looking good for us!