What is the legal test for public financing of political campaigns in the United States?

The Buckley v. Valeo case dealt with many aspects of political contributions in the United States, one of which was subtitle H of the Internal Revenue Code of 1954, which provided (at p. 626): ... for public financing of Presidential nominating conventions and general election and primary campaigns from general revenues and allocates such funding to conventions and general election campaigns by establishing three categories: (1) "major" parties (those whose candidates received 25% or more of the vote in the most recent election), which receive full funding; (2) "minor" parties (those whose candidates received at least 5% but less than 25% of the votes at the last election), which receive only a percentage of the funds to which the major parties are entitled; and (3) "new" parties (all other parties), which are limited to receipt of post-election funds or are not entitled to any funds if their candidate receives less than 5% of the vote.