Seems to be missing some short names --- for instance, while diiq.com and diiq.org are owned, diiq.net is unclaimed --- but 'diiq' does not appear at all, despite being four characters long. What qualifies a domain name to appear in your list?
My list is a fairly random sampling of the huge search space of available domain names. I'm planning to keep adding more names in the future, trying to strike a balance between good names (short but readable) and more names (requiring more storage). Fortunately, the App Engine Datastore has linear complexity for the number of query results, so adding more names doesn't slow down the searching.
Because we can't run DNS queries inside Google App Engine. Instead, I query the DNS results from my home computer and feed them into the datastore using remote_api.