Mixed Radix Encoding (Optimal Entropy)

I find that we often use whole bytes when bits can suffice, and use bits when fractional bits can suffice. A mixed radix encoding is the optimal way to encode a series of quantities with different cardinalities.

The factorial number system (used to number permutations) is one such example of a mixed radix system.

However, the radixes you most commonly encounter, tend to have monotonically increasing radixes -- this is not necessary though, and we can choose even complex numbers as our radixes. The only necessity is to derive place values through the product of the radixes (this way each place value is greater than the previous.)

https://en.wikipedia.org/wiki/Mixed_radix#Factorial_number_s...