[deckar01]

I think you are focusing on the wrong number.

Each byte of base64 produces 6 bits of data, so the boundary aligns at 32 bits. LCM(6,8) = (6•8)/2

Each byte of base122 produces 7 bits of data, so the byte boundary aligns at 56 bits. LCM(7,8) = (7•8)/1

Edit: Due to the variable length encoding, there is no guarantee of byte alignment.

[beagle3]

If it was base 128 it Would have produced 7 bits. But as it is 122 it produces 6.8 bits, hence a problem.

[deckar01]

> This uses one-byte characters encode seven bits and two-byte characters to encode fourteen bits. Hence this attains the goal of encoding seven bits per byte, i.e. the 8 : 7 inflation ratio.

The magic is in the 2 byte encoding 110sss1x 10xxxxxx.

There are really 890 characters used in this encoding, so it should be called base890.

((2^7)-6)+((6•2)•(2^6))=890