What does it mean if there is an asterisk next to the psat selection index score

What is the National Merit Scholarship Program and how do you enter?

The NMSP is a program administered by the National Merit Scholarship Corporation in cooperation with the College Board to recognize high achieving high school seniors. Some recognition levels are based purely on junior PSAT/NMSQT scores, while other levels have additional qualifications (explained below). The NMSC gives out approximately $50 million in scholarships each year, and some colleges provide lowered - or even free - tuition for recognized students.

You must take the PSAT/NMSQT as a high school junior and meet certain citizenship requirements. On your PSAT score report, you will see a section with your Selection Index and how you answered the questions about your entry eligibility. If there is an asterisk next to your Selection Index, it means that NMSC believes that you are ineligible.