On a dusty, gusty plain in northeast Wyoming, a nondescript patch of public land has spawned one of the strangest mysteries in the troubled history of the federal oil and gas lottery.

The FBI, the Interior Department and a House committee are investigating how the government awarded drilling rights on federal land tract W-698. Interior says no misconduct has been found, but it has stopped issuing drilling leases and launched a study of its mineral leasing operation while investigations continue, according to Mark Guidry, a spokesman for Interior's Bureau of Land Management.

Every other month, the Bureau of Land Management holds a random drawing, or lottery, for oil and gas leases on scattered tracts of federal land where oil and gas reserves have not been identified.

Last spring, SECO Energy Corp. of Casper, Wyo., wrote the government asking that a 2,530-acre tract, labeled "W-698" on the official maps, be included in the lottery. But BLM officials here decided that W-698 could not be included and denied the request.

Another oil executive from a different company then appealed to the BLM's top official here, Hillary A. Oden, to have W-698 included. Oden subsequently met in Washington with his boss, BLM Director Robert F. Burford.

Returning from Washington, Oden directed his subordinates to reverse their decision and add W-698 to the list of oil leases to be awarded in the lottery. Otherwise, Oden said, "Burford and three congressmen will be on our back."

Thus Tract W-698 was included in the October 1984 lottery, as SECO had requested. More than 400 individuals and firms, including SECO, entered the drawing for that tract.

And the winner was: SECO Energy Corp.

"It's an amazing, amazing coincidence," said a government investigator who has been pursuing the matter. "But from all we can find, it is nothing more than a coincidence."

Oden, the Wyoming BLM director, agrees that SECO's success in the lottery was "just a coincidence."

The coincidence was so striking, however, that employes in the Cheyenne office of the BLM raised questions with their superiors, the Justice Department and congressional probers.

The mystery of W-698 comes at a time when the bimonthly federal oil and gas lottery is under fire. The lottery has been suspended three times in two years because of fraud allegations. At a congressional hearing last month, Interior officials promised to design a completely revamped lottery system by this summer.

Critics have urged the administration to forgo the lottery and distribute leases through the competitive bidding used for tracts where oil or gas reserves have been identified.

The lottery is extremely popular among independent oil and gas companies. They say they couldn't compete for leases if they had to bid against the major oil giants. This pressure has made the lottery a political pet for many members of Congress.

The investigations of W-698 have dealt with two questions: whether there was political pressure to include the tract in the lottery, and whether the random drawing on that tract might have been rigged.

The Interior Department has not made the report of its investigation of the W-698 lease available to the public. Spokesman Guidry said the report found that no political pressure was brought to bear. As for the lottery's integrity, he said, the report concludes that because of lax computer security it would have been possible to manipulate the drawing.

Oden, in the BLM office here, said his warning that Washington officials "will be on our back" was "an unfortunate phrase that I used." He said he used those words not to influence any specific decision but rather to emphasize the general need to put oil and gas tracts up for lease and thus encourage exploration.

"It was in the context of, hey, if we don't get these, get this leasing system going," Oden said, "get tracts up, you know, that people would like to see, hey, I'm in trouble as far as what my objective is . . . that people can have an opportunity to try to find some more domestic oil and gas."

Oden said that his reference to "three congressmen" was hypothetical and that he had no specific politicians in mind.

Burford, the BLM director, said through a spokesman that he never pressured Oden or anyone else to add tract W-698 to the lottery.

SECO's president, Richard Stevens, said that "somebody had to win the lottery, and we had the same chance as everybody else . . . . We're completely innocent." A federal investigator said there is no evidence of wrongdoing on SECO's part.

Interior has refused to issue SECO the lease it won until all investigations are complete. And last month, after receiving a preliminary report on the W-698 matter, Interior suspended issuance of any oil and gas lease obtained through the lottery.

The federal government owns hundreds of millions of acres in resource-rich areas of the South and West. The Interior Department works hard to sell oil and gas drilling rights, or leases, on this land, both to bring income to the Treasury and to encourage exploration and development of domestic energy sources.

Under the Mineral Leasing Act of 1920, any federal land likely to contain profitable oil or gas reserves is leased through competitive bidding. Energy companies pay the government $5 to $5,000 an acre per year for the right to drill on such land; if oil is found, the driller pays the government a royalty up to 25 percent of earnings.

The great majority of federal land, however, has no known oil reserves. The government awards drilling rights on such land chiefly through its bimonthly lottery.

The Bureau of Land Management lists about 1,800 tracts every other month that anyone -- oil firm or individual -- has a chance to win. To enter the lottery requires an entrance fee of $75 per tract. The winner of the drawing on any tract must pay the government a lease fee of $1 an acre per year for the first five years and a royalty of 12.5 percent on earnings from the well.

Most of the tracts included in the lottery come from government lists, but it is not uncommon for a firm like SECO to ask that a particular tract be listed.

When that happens, the government has to decide whether the tract has known reserves. If so, the tract is ineligible for the lottery. Its lease must be sold through competitive bidding, which is more expensive for the lease buyer. A.A. Phillips of the Independent Petroleum Association of the Mountain States said oil firms would rather get a tract through the less expensive lottery than through bidding wars.

One of the biggest recent controversies in the lottery erupted in 1983 when the BLM leased, at the $1-an-acre lottery rate, oil rights that later sold for $10,000 an acre on the open market. Later investigations by the BLM and General Accounting Office concluded that these leases should not have been included in the lottery.

The drawing of lots to determine the winner for each tract goes on inside a computer at Interior's regional office in Denver. According to BLM officials, each applicant for a tract is assigned a number, and the computer generates numbers at random until its number matches that assigned to one applicant.

The case of W-698 began last spring when BLM officials here were preparing the list of tracts for the October 1984 lottery.

SECO sent two letters asking for inclusion of land southwest of Gillette, Wyo. -- tract W-698. Stevens, of SECO, says his firm had other leases near that land and wanted a chance to control a larger region before drilling.

But when BLM officials first investigated W-698, they decided that it was a likely prospect for oil reserves -- and that the tract was therefore too valuable for disposition in the lottery.

Oden, who later overturned this decision, said that determination was based on the presence of an oil well near W-698. He said further research showed that this well was dry, and thus there was no evidence that W-698 had oil reserves.

Oden said he asked his subordinates to do further research on W-698 after he got a call from an executive of True Oil Co., another firm interested in winning a lease on that tract. Oden said they found no evidence of oil reserves, and he directed them to include the tract.

A House investigator on the case says the fact that two firms expressed interest in that piece of land should have demonstrated that W-698 was too valuable to be given out in the lottery.

Oden said he was not aware that two different firms had asked to have W-698 added to the lottery list.

Once W-698 was listed, 405 applicants paid the $75 fee for a chance to win drilling rights on the tract. Thus the odds were 1 in 405 that SECO would win.

"It's within the laws of probability that SECO would win ", Oden said. "That's all I can say."

At the Justice Department's request, the computerized lottery for W-698 was run again to see if SECO's victory was indeed a random event. In this test run, SECO did not win. Investigators say that indicates that SECO's win in the drawing was luck.

Nonetheless, Interior's inspector general concluded in an audit that the lottery computer system was not adequately protected against potential skulduggery.

"We concluded that because of poor internal controls and the lack of audit trails in the automated process, we could not prove that the . . . system was manipulated to the benefit of one or more applicants," Interior auditors said in a report issued March 29. "Because of the same weaknesses, we do not have confidence that the drawing was not manipulated."

Oden and Guidry say that Interior is implementing a marked increase in security procedures at its computer operation in Denver. Among other things, the password needed to get into the computer system will be changed periodically. Previously, a department spokesman said, the password was rarely changed, even when a computer operator left the government and went to work for an oil firm.

Although investigations of the W-698 affair are proceeding, government investigators now say it is unlikely that the result of the lottery will be reversed.

"After all the investigations are finished, I assume the lease will be awarded to SECO," Guidry said. "After all, they won it, didn't they?"