The latest news on this front comes from a really interesting article at Ballot Access News written by the widely-respected election expert and advocate for third party/independent ballot access Richard Winger:

On June 9, briefs on both sides were filed in the Georgia Libertarian Party ballot access case that challenges the requirements for parties that did not get 20% of the vote for president or governor in the last election to be able to run candidates for U.S. House. These procedures require a petition of 5% of the registered voters in the district. They are so difficult, they have existed since 1943, and have never been used by any party. No independent has complied with the law since 1964.

Both sides are seeking summary judgment. If the judge decides that either side has proved its case, she will either uphold the law or declare it unconstitutional. If she decides in favor of neither party, she will hold a trial.

Winger also conveniently added a link to the Libertarian Party’s brief and the state’s brief.