Virginia Gov. Charles S. Robb and state legislators relied upon an outside consulting firm's report that contained more than $39 million in arithmetical errors when they decided not to give state employes a general pay raise in the recently passed state budget, state officials and spokesmen for the consulting firm acknowledged today.

As a result of the errors--which were made by the Washington office of Hay Associates, a prestigious international consulting firm--the General Assembly is expected to reopen debate on the budget at a special veto session April 21 to consider how much to increase the salaries of 73,000 state employes and where to find the money.

The Hay firm had been awarded a$140,000 noncompetitive contract by the state last November to study how state salary levels compare with those in the private sector. Its draft report, submitted to state officials in February, overstated the salary levels of56,000 state employes sampled by an average of $700 per person because of mistakes in division, officials said.

"It's incredible, it's preposterous," said Wayne Anderson, secretary of administration and finance. "No one who has seen this can believe they made that made such an error. . . . It's provoking, frankly, when a consultant's errors makes their work valueless and does damage to the government."

Robb said today that he had asked Attorney General Gerald L. Baliles to study the terms of the contract to determine whether the state is still obligated to pay the Hay firm. No payments have yet been made under the contract, state officials said.

"Whether the full amount will be paid is an open question at this point," Robb said.

"What happened was a very, very, very regrettable error," said David Wimer, general manager of the Hay firm's Washington office.

But Wimer said the firm had put in "an enormous amount of time and money" in working around the clock to correct its errors. "Since they are using a great deal of the information, it seems to me that its appropriate that it deserves payment," he said.

Because of the overstatement of state salaries, the Hay Associates report concluded that Virginia is paying its workers, who average $14,539 a year, comparable salaries to private businesses in the state. As a result, Robb and the General Assembly rejected as too costly a recommendation by the state personnel department that state workers receive a 4.5 percent across-the-board salary increase, which would have cost $70.3 million in the state's two-year budget.

Instead, Robb proposed--and the legislature accepted--a more modest $40.8 million proposal for selective pay adjustments for managerial and professional employes.

While emphasizing that he had made no final decisions, Robb said at a news conference that he is considering a "number of options," including asking the legislature to find an additional $30 million elsewhere in the budget for an across-the-board pay increase.

State officials today described the report's errors as simple mistakes in arithmetic that could have been caught by any reasonably sharp sixth grade student. According to the officials and consultants who worked on the study, the Hay firm attempted to compute the average salaries for state employes in 93 different categories, ranging from custodians to mental health doctors.

To compute the averages in each category, the firm sampled the salary levels for each job in three geographic areas--in Northern Virginia and in Loudoun County, where the state pays a 5 to 20 percent differential because of the higher cost of living, and in the rest of the state. It then computed the average for each job by adding together the salaries in each area and dividing by three.

But this figure was inflated, officials said, because the firm failed to weight its equation by taking into account the lower number of higher paid employes in Northern Virginia and Loudoun compared with the rest of the state. For example, in the case of one category of clerk-typists, there were 215 employes in Northern Virginia earning $12,289, three in Loudoun earning $12,597 and 3,051 in the rest of the state, earning $10,801.

The Hay firm added the three salary figures ($12,289 + $12,597 + $10,801 = $35,687) and then divided by three to reach an average of $11,896.

In fact, state officials pointed out, to get a true average the equation must be weighted by multiplying the number of employes who receive each salary figure. When this is done in the case of the clerk-typists, for instance, the true average is $10,901, or $995 lower than the Hay firm's average.

Wimer said the employe who made the error and "fed the wrong numbers into the computer" was a senior consultant who had been with the firm for many years. He refused, however, to identify the employe. "I would imagine the person won't be with us for very long," he said.