LONG BEACH – The state's largest university system has agreed to shut out at least 20,000 qualified students next year.

Closing the higher-education door to the 410,000-student California State University system is a result of the newest round of budget cuts by Gov. Arnold Schwarzenegger. CSU trustees concluded yesterday that because of the state's financial crisis, they had to accept the Republican governor's $240 million cut to the system and limit enrollment to compensate.

And CSU officials haven't ruled out agreeing to the governor's proposed tuition increases, which range from 10 percent to 40 percent. The fee increase will be considered in March.

Last year, the university system raised fees by 40 percent, one of the largest increases in the nation.

"It's still very early in the game. We don't know how this will play out yet," said San Diego State University President Stephen Weber.

SDSU, one of the most crowded universities in the 23-campus system, will limit its applicant pool and accept 6,000 to 7,000 students.

The demand for higher education rises in bad financial times and the demand for SDSU has never been higher, Weber said. Despite the shortened application period that campuses have been using to keep enrollment down, San Diego State received more than 44,000 applications for next fall's academic year.

"That's 44,000 folks circling the airport for maybe 6,000 or 7,000 open spaces," said Weber, who said the university would have to raise the enrollment standards to handle the crush.

CSU officials said they would limit enrollment for the third year in a row. They said an estimated 20,000 students who meet CSU eligibility requirements won't be accepted.

The pain will be felt for current students as well, who will experience larger classes and fewer course sections and support services.

Trustee Ralph Pesqueira of San Diego worries that the state's crisis will continue to bleed resources from the university system. "We're worrying about '04-05; let's talk '06-07 and beyond. Students have every right to point out that the state of California made a promise of free education. And that promise is no longer there."