Knuth has a "hugenum" scheme, TCALC, which is based on trees rather than byte arrays. There are many ways to do it, depending on which type of numbers you need most - for TCALC, it's numbers close to towers of exponents.

Of course for every big number encoding that can beat an array of bytes for some numbers, it also has to lose to byte arrays for some numbers... But it's possible to bound this inefficiency, so that it's never more than twice as bad as byte arrays, but potentially exponentially more efficient for the favoured numbers.