LINCOLN, Neb. — The owners of four now-closed stores that sold millions of cans of beer next to an American Indian reservation where alcohol is banned are fighting a steep Nebraska tax bill.

An audit by the Nebraska Department of Revenue determined the shuttered stores owe more than $600,000 in taxes and underrepresented nearly $1.7 million in sales from August 2013 to August 2016. The stores closed in April after the Nebraska Liquor Control Commission denied the renewal of their liquor licenses following concerns that local law enforcement was inadequate to allow beer sales to continue.

The four stores are in the tiny village of Whiteclay, Nebraska, on the border of the Pine Ridge Indian Reservation in South Dakota. The reservation is plagued by a litany of alcohol-related problems, including high rates of fetal alcohol syndrome, and activists complain that Whiteclay fuels those issues. The village has only a handful of residents, yet sold the equivalent of about 3.5 million cans of beer annually.

Owners of the shuttered shops — Arrowhead Inn, State Line Liquor, D&S Pioneer Service and Jumping Eagle Inn — have asked a judge to review the audit's findings, the Lincoln Journal Star reported . The owners say the review was based on incorrect estimates. Their attorney filed nine petitions for review on Friday alleging the department's decisions were "arbitrary, capricious and/or unreasonable."

Department auditors first reviewed the books of individual stores and then conducted on-site audits in September 2016, according to court records. Auditors were looking for documentation to support the sales and use tax returns the stores reported. However, the state Liquor Control Commission had taken those records, so store owners weren't able to provide the documentation.

Auditors instead took the alcohol suppliers' records of all sales to the businesses during the audit period, which auditors used to reconstruct sales.

Store owners argue that the records don't show if packs of beer delivered to the store were broken down and sold as singles or in their larger packs. Owners say the audit also didn't take into account wholesale price increases or provide an accurate number of individual can sales.