The long-running case was brought by a white woman named Abigail Fisher, who claimed she was denied a spot at the university because of her ethnicity.
The court ruled against her by a narrow majority of four to three, one of its eight sitting justices having recused herself in the closely-watched case.
Fisher graduated from a different institution in 2012. But her case continued its way through the courts. It reached the Supreme Court in 2012, but the justices sent it back to a Texas appeals court for review.
It reaffirmed that finding in 2003, but stipulated that so-called affirmative action is legal only if racial quotas are not used.
The University of Texas, carefully threading that needle, devised a policy guaranteeing admission to high school students graduating in the top 10 percent of their class.
Most students at the university are admitted under the so-called "Top 10 Percent" program which itself has produced significant racial and ethnic diversity.
But Fisher's challenge concerned another part of the admissions program, which takes into account athletics and other extracurricular activities -- as well as ethnicity.
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