Libertarian government is pretty much an oxymoron. Libertarianism applied in that sense is anarcho-capitalism, where everyone is free to do as they please and the only controlling force (i.e. the law) is the free market - no gov't at all. There are some people like David Friedman who have tried to make the case for how such a system could realistically work, but I'm still unconvinced (largely because the wealthy will have a monopoly on force).

I'm more a fan of his father, Milton, who was very pragmatic and not totally against gov't.