BY VIRTUE of absolutely nothing other than their being the respective presidential nominees of the Republican and Democratic parties, Ronald Reagan and President Carter have each received (and cashed) a U.S. Treasury check for $29.4 million. No other presidential candidate, regardless of debate invitations or standings in public opinion polls, will receive a dime of public money before the November election.

But thanks to a recent decision of the Federal Election Commission, presidential candidate John B. Anderson may very well qualify for a government check sometime after the votes are counted. The Election Reform Act of 1974, which established both the principle of, and the formula for, public financing of the major-party presidential campaigns, also provided for post-election reimbursement of third-party candidates who managed to win more than 5 percent of the national popular vote.

Prior to the balloting, if any of the usual four dozen third-party presidential candidates wants to purchase a balloon, a campaign brochure or 30 precious seconds of television advertising during a World Series game, then that candidate can raise the necessary funds only through individual contributions in amounts not larger than $1,000.

What the Federal Election Commission decided was to treat Rep. Anderson, who is an independent candidate for president, as if he were a political party -- which he is not. For a lot of reasons, including the fact that it is easier in many states to get on the ballot as an independent candidate as a new political party, Mr. Anderson announced early in the campaign that his was not a new party but rather an independent candidacy. Through its decision, which was sought as well as welcomed by the Anderson campaign, the Federal Election Commission has made John Anderson into someone who just might come into his own windfall grant if he wins a healthy percentage of the vote on Nov. 4.

Here is how it all works under what must be one of the most truly straightforward federal formulas ever devised. Add the percentage of the national popular vote received by both the Democratic and the Republican tickets, and divide by two. With this new percentage, we have the denominator for what we shall call our Reimbursement Fraction. The numerator is the percentage of the national popular vote that the third-party candidate won. So if, for matters of discussion, Mr. Reagan and President Carter were each to win 40 percent of the popular vote, and Mr. Anderson were to win 20 percent, then the equation would be 20/40, or one-half. That is what Mr. Anderson would then be entitled to in the way of reimbursement: one-half of the $29.4 million the Democrat and the Republican each received. Mr. Anderson could have a Treasury check for $14.7 million as a consolation prize.

With the encouraging poll results and the prospect of a post-election check, Mr. Anderson's agents are reportedly looking for a really bullish banker to lend the campaign cash for immediate purchase of television and radio advertising to compete with the "Big Two," who are both reportedly devoting better than half of their $29.4 million to such advertising.

If Rep. Anderson actually ends up this race with more money than he has spent, then he would face the very real option of being able to do what he said he had no intention of doing when he launched his independent candidacy -- start a real and even semi-permanent third party -- and do it with a form of federal reward for having been a successful independent.