Kansas City, Kan. ? An expert witness for Secretary of State Kris Kobach in a trial over Kansas’ voter registration law defended his own estimate that up to 18,000 noncitizens have voted in Kansas, but said he couldn’t support Kobach’s claim that more than 3 million noncitizens voted in the 2016 presidential election.

Jesse Richman, an associate professor of political science at Old Dominion, endured intense questioning about his numbers from Dale Ho, an attorney for the American Civil Liberties Union, The Topeka Capital-Journal reported. Richman has offered various estimates, ranging from 1,000 up to 18,000, based on surveys he conducted, and Kobach has said the 18,000 estimate is the best available number to show the law is needed to address widespread voter fraud.

The ACLU is challenging a 2013 Kansas law that requires documents proving citizenship when registering to vote, and the outcome of the trial could determine if thousands of Kansans will be allowed to vote.

Richman said he based his estimates on surveys he’s conducted, although he acknowledged under cross-examination that his work was not peer reviewed and that 200 political scientists signed a letter criticizing his work.

In one survey, Richman and a graduate assistant flagged names on the list of suspended voters in Kansas that sounded foreign. When Ho asked if the name “Carlos Murguia” would be flagged, Richman said yes. Ho told him Murguia is a federal judge in the courthouse where the trial is occurring.

Under questioning from Kobach, Richman said he concentrated on finding foreign-sounding names to avoid incorrect sampling of people from different demographics and that he was not drawing conclusions about people’s nationality.

Ho showed a video of Kobach being interviewed by reporters in November 2016. In the video, Kobach defended a survey that said 11.3 percent of noncitizens reported voting in the U.S., which would mean at least 3 million illegal votes out of the estimated 28 million noncitizens nationwide. After the video, Richman said his study doesn’t support that claim, and he isn’t aware of any research that does.

Richman’s tense exchanges with Ho continued a strained atmosphere in the six-day trial, which included several angry exchanges between U.S. District Court Judge Julie Robinson and Kobach’s legal team.

Richman and Kobach have disagreed with Robinson’s decision to exclude estimates of the number of noncitizen voters in Kansas that were updated from the 127 names presented before the trial began. Robinson and Kobach’s team also have clashed repeatedly on Kobach’s efforts to introduce evidence that was not offered before the trial began.