Actually, few MUDs are going to have more than, say, 300 players most days. Since storage expands quadratically (not exponentially) in the number of players, say that's 900000 bits for whether you know somebody. That's less than 900kB.
You could make it *much* smaller by runlength-encoding your string of bits. That means that people who knew almost everybody and people who knew almost nobody would both have really small representations for who they knew.
If you do it right it's quite fast. That's how the original Quake did its visible surface lookup, roughly.
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