There is no one universally best compression algorithm. Different algorithms have been invented to handle different data.
For example, JPEG compression allows you to compress images quite a lot because it doesn't matter too much if the red in your image is 0xFF or 0xFE (usually). However, if you tried to compress a text document, changes like this would be disastrous.
Also, even between two compression algorithms designed to work with the same kind of data, your results will vary depending on your data.
Example: Sometimes using a gzip tarball is smaller, and sometimes using a bzip tarball is smaller.
Lastly, for truly random data of sufficient length, your data will likely have almost the same size as (or even larger than) the original data.
