A headline in yesterday's Post incorrectly stated that Fairfax County officials are seeking a tax increase to fund the county's fiscal 1982 budget. The proposed budget, which must be approved by the county supervisors, would be funded by rising property tax assessments and not an increase in thereal estate tax rate.

Fairfax County Executive J. Hamilton Lambert, anticipating that Ronald Reagan will succeed in slashing millions of dollars in federal aid to the county, yesterday proposed a $509.3 million budget for the coming fiscal year that will boost real estate taxes on the average home by $168.

Lambert's proposed budget depends on rising property assessments -- up by an average of 14 percent over 1980 levels -- largely to fund the county's spending at current levels and to give its workers a 9 percent pay increase. His budget would also create a $6.6 million contingency fund to cushion the impactof less federal aid, including an anticipated loss of $9 million in federal impact school funds that Reagan is proposing.

The budget is the first example of how Washington areagovernments are going to react to Reagan's budget cuts. Itseems to bear out the predictions of some opponents of the Reagan plan who have warned that local governments may offset the cuts by boosting local taxes.

Fairfax officials said yesterday they expected that their contingency fund would cover only a portion of the federal money that the county will lose. "We have to set our tax rates by May 1and I can't imagine that the federal government will know by then exactly where they will be making their cuts," said Deputy County Executive James P. McDonald, "so really all we can do is make contingencies the best we can and then hope."

Fairfax Board Chairman John F. Herrity predicted that homeowners "willreceive the budget with a great deal of dismay. (The budget) has held the tax rate steady but with the increase in assessments people are still paying more. That's the eternal problem."

Impact aid, funds that the federal government grants to localities that have large concentrations of federal workers, has been an annual target of budget cutters since its inception in 1950. But this time, impact aid is facing what is believed to be its most severe test. "What is new," said James W. Maza, an official of a school group that has lobbied to retain the funds, "is the mood of the nation and the Congress."

Under Reagan's proposal, only school districts where at least 20 percent of the children's parents both work and live on federal property (primarily Indian reservations and a few military bases) will be entitled to benefits. Only 1.2 percent of Fairfax's 125,500 students, most of whom live on the Army's Ft. Belvoir, fall into this category.

As a hedge against the loss of such federal aid, Virginialegislators recently approved legislation that would enablelocal governments to charge tuition for children for whom the school systems now receive impact aid. If used, said Fairfax school official Myron Cale, the legislation "would end up costing (military) families twice as much--$2,833 per pupil--as the government now pays us."

At present, Fairfax receives more federal impact aid than any other Washington jurisdiction. In addition to the $2.5 million Fairfax receivesfor educating 1,520 Ft. Belvoir students, the county receives $4.8 million for 24,400 military students who live elsewhere in the county and $1.1 million for some 8,000 children whose civilian parents work on federally-owned property.

"We think the president has been misinformed," said Cale, "and we intend to inform the administration and our representatives in Congress that a mistake has been made. This is not in our judgment a viable budget cut. Let them look elsewhere."

The budget will be reviewed and possibly revised by both the supervisors and Herrity before it is approved.

Other features of County Executive Lambert's proposed budget, which he characterized as one that features "maintenance of service and minimization of expenditures," were:

Property tax rates that remain the same $1.54 per $100 of assessed valuation. But assessment increases will mean, based on a typical home valued at $88,686 -- up from $77,795 a year ago -- that an average real estate tax bill will be $168 higher.

Sewer rates that will be higher, $17 a year for the averagefamily. The increase will be needed to fund the costs of advanced waste treatment systems, higher fuel and chemical costs and new, more stringent federal standards for waste treatment.

Educational spending up 18.5 percent over 1980 levels, up to $256 million.

Metrorail and Metrobus services budgeted for a 2.9 percent increase, up to $17.1 million. This, said Herrity, along with the increased school budget and fears of losses of federal aid, "is very disturbing . . . The best hope as I see it is to develop our own bus system.Metrorail is a given, but two thirds of the $1.7 million goes to buses.I think we can do it more efficently on our own."

Creation of 128 new jobs, mostly in public service andlaw enforcement at a cost of $2.2 million. An additional reserve of $1.4 million is also included to fund new equipment and positions required to open the new county courthouse in Fairfax City.