I did a recent scan of available LLL domains. None are available.. I would like to share this list with you of all available domains in: LL# combinations. Sorry, no .com or .net LLL's are available at this time that the tool scanned. Just .gov, .info, .cc, .us & .mobi Soon the tool will auto-refresh web 2.0 Design Style with AJAX, as best as it will / can so the alerts are immediate. I am willing to share this PHP tool as seen now. As you can see, it constantly monitors for LLL available domains. but it takes it days to spawn from A-Z & 0-9 etc.. Then for the next cycle.. You must start from axx - axx.. etc.. The tool has a means of setting the start letter or number. Say axx.xxx to zxx.xxx Let me know if you'd like this source. http://www.expron.com/fxx.htm
You can register .GOV's at any usa registry. A few are: godaddy, register.com, namecheap, network solutions, aitdomains & more. As far a the cheapest, i'm not sure... But if i'm not mistaken, aitdomains.com & hostingplex.com allow these .GOV domains to be registered by non-usa residents. Just in case you're out of the country.
From http://www.dotgov.gov On another page: It's not the only domain to have restrictions. .fed and more also have restrictions. Isn't .us only for US and canada? etc.