The number of petitions for H-1B temporary workers filed for next year increased overall by about 20 percent this time around, U.S. immigration officials said this week.

On Tuesday, U.S. Citizenship and Immigration Services said it had closed this year’s application window, having received more than enough petitions to meet a congressionally mandated cap of 65,000 visas and fill another 20,000 slots for foreigners holding advanced degrees from U.S. universities. But it didn’t immediately reveal the number of petitions it had received.

USCIS said on Thursday that according to a “preliminary” count, it had received more than 163,000 petitions, of which about 31,200 pertained to the visas for advanced degree holders, between April 1 and April 7. Per a recent rule, USCIS plans to conduct a random computer selection process to narrow down the petitions received during those first five days of the application window.