The outgoing Carter administration yesterday recommended a record high federal payment of $336.6 million in its 1982 budget proposal for the District of Columbia.

Based on a modified version of a formula suggested by city officials, the proposal is $35.1 million above the amount proposed by the White House a year ago, and $41.2 million greater thanthe $295.4 million payment finally approved by Congress last year.

Even if the new Republican administration supports the higher payment -- and its views on the matter are not known -- it is unlikely the final appropriation will go much beyond the 1981 figure unless Congress votes to lift the present $300 million ceiling on the payment. u

The payment is made to the city annually in lieu of taxes that the local government cannot impose on the vast number of federal buildings and foreign missions that occupy nearly half of the land area of the city.

City officials have been urging Congress to approve some formula or fixed basis for the payment so that District Building budget officers can know on a regular basis how much money it can rely on, but Congress has so far resisted this, even though the Carter administration favors the idea.

The new chairman of the Senate subcommittee on the District, Sen. Charles McC. Mathias (R-Md.), has said he opposes a fixed formula, believing that the payment "ought to be the result of negotiation" between Congress and the city.

The final Carter budget proposes ending the city's ability to get interest-free cash advances from the U.S. Treasury, saying that it is time for the city to start borrowing in the private bond market, a provision of the 1973 Home Rule Act, which the city has so far not exercised.

Another Carter proposal would eliminate payments to all Washington-area school districts under the impact aid to education program. The program compensates local schools across the country for the loss of property tax revenue that results from the presence of tax-exempt federal land or large numbers of federal employes in their districts.

Because of the large number of federal employes in the Washington area, the program has been a boon to area school districts. But under proposed tightened guidelines, the only school systems that would qualify for impact aid would be those in which at least 20 percent of the students are children of persons who both live and work on federal installations.

The big hope of area school administrators is that Congress will come to the rescue, as it has every year for the last 20, and restore at least part of the program.