then by all means show me a sequence of fewer than 10 digits that contains every number from 0-9. Because that is what you are claiming is possible. Your index will always take more bits, because you cant say well, I found 14159 at index 2 so my index only takes 2 bits. Because you cannot find arbitrary sequences, that means any sequence I happen to need compressed, such as 27894 using only a 2 bit index, therefore your index must mathematically be large enough to contain an index sufficient to find ALL possible sequences of say 5 numbers. Plus you have to somehow encode the run length, either by having all symbols be of fixed length, or by encoding it as part of the index. Even in those cases you can never achieve better than parity. If you had actually read my previous posts you would understand why.