The federal judge hearing a lawsuit that alleges racial discrimination in Boston's new, temporary plan for admission to the city's exam schools sounded notes of skepticism Tuesday about the case brought by a group of Asian and white parents.

The suit, filed by the Boston Parent Coalition for Academic Excellence, argues that a plan the school committee adopted for this fall is an "unconstitutionally race-based system" that disadvantages white and Asian students. Under the plan, 20% of seats in Boston Latin School, Boston Latin Academy and the John D. O'Bryant School of Mathematics and Science would be filled in rank order by grade point averages achieved before the pandemic. The remaining 80% would be allocated to students with qualifying GPAs based on zip codes, with those who live in the lowest-income zip codes getting to choose first.

U.S. District Court Judge William G. Young held a virtual hearing Tuesday to determine filing deadlines and set a date for a trial, which he scheduled for April 6. He is hearing the expedited case without a jury and expects to issue a decision by April 15 so the school department can assign students to the three exam schools.

The lead counsel for the parents group, William Hurd, told Young that his clients were ready for a trial after the parties Monday submitted a 19-page outline of facts they all agree to. The judge told the lawyers assembled on Zoom that he did not intend to hear arguments Tuesday, but Hurd slipped into them on ocassion.

"The purpose of the zip code plan is to achieve racial balancing," said Hurd, who works for a law firm based in Richmond, Va.

"Wait a minute — maybe," Young replied.

At other points in the hearing, the judge suggested that assigning students based on zip codes did not appear to be discriminatory on its face.

"The use of zip codes seems truly race neutral," he said. "It doesn't pit one race against another. It makes competitive students in that zip code."

Young said the plan would make make students assignments "in a mechanistic fashion" based on "objectively established" factors. "There is no back room where students are compared one to another," he added. "No racial markers are used."

The judge also questioned the parents group for invoking a U.S. Supreme Court opinion of four justices in a 2007 case that involved student assignments in Seattle and Louisville. Young said a concurring opinion by retired Justice Anthony Kennedy is considered to have decided that case against the school districts. "I have some questions about citations of the plurality decision as if it were a holding," Young said.

Hurd signalled his team plans to argue that the school committee's intent was shaped by racial considerations.

"We have to show only a racial motivation, benign though it may be," he said. "This plan imposes a disparate impact upon Asian and white students of Boston."

Young allowed the Anti-Defamation League to enter the case as a friend of the court, siding with the school committee.

Correction: This story has been corrected to indicate Justice Anthony Kennedy is retired from the US Supreme Court.