They get down to about 100bp. All they need is the gene encoding the enzyme needed to insert or cut them from the host genome (a transposase), genetic control elements to ensure it gets expressed in the host (can be just a tiny promoter), and the recognition sequence for the transposase at either end of its genome. It's basically the precursor to viruses - parasitic replication, but without any structural elements needed.

If you consider viruses alive, then the answer is a transposon. It's just the bare minimum genetic sequence needed to reproduce parasitically. Sorry OP, the answer depends on your definition of life - I hope you enjoy discovering where your definitional lines are drawn!