A storage system includes a storage medium operable to maintain a data set, a read/write head assembly operable to write the data set to the storage medium and to read the data set from the storage medium, a multi-level enumerative encoder operable to encode the data set before it is written to the storage medium as encoded data, wherein the enumerative encoder applies an enumeration using a plurality of level-dependent bases, and a decoder operable to decode the data set after it is read from the storage medium.