How does a society with a Libertarian Socialist structure work?

Granted I'm not a government specialist, but it would seem in my mind that those two doctrines (socialism and libertarianism) are diametrically opposed to each other. Whereas Socialists generally favor heavy government involvement in both governing bodies and the private sector, Libertarians usually try to contain government as much as possible. Both parties would rely on the government to enforce the law, and innovation would occur, however with the Libertarians, they would more more in favor of letting the free market dictate what innovations succeeded or were used. I honestly can't think of any societies such as this, as they are opposing viewpoints, and any society like this would probably get little accomplished.