Indianapolis Cincinnati, Maryland, Michigan and Louisville were seeded No. 1 Sunday in the revamped National Invitation Tournament.
Also among the 40 teams selected for the NIT were six that won regular-season championships but lost in their conference tournaments and weren't picked for the NCAA Tournament.
The NCAA bought the rights to the NIT in August as part of a settlement ending their four-year legal battle. Among the changes in the selection criteria, all Division I conference regular-season champions who weren't in the NCAA's field of 65 were guaranteed NIT bids.
The opening round of eight games will begin at campus sites Tuesday.
It's the second straight year Maryland missed the NCAA and went instead to the NIT. The Terrapins reached the semifinals of the tournament last year before losing to eventual champion South Carolina.
"It's a tough thing, because I thought our guys did a good job this year to win 19 games," Maryland coach Gary Williams said. "A lot of times 19 wins are rewarded by going to the NCAA."
Instead, the Terrapins (19-12), who lost in the quarterfinals of the Atlantic Coast Conference tournament to Boston College, will play a first-round game Saturday against the winner of Tuesday's game between Metro Atlantic regular-season winner Manhattan and Northeast Conference winner Fairleigh Dickinson.
Michigan (18-10), which lost in the first round of the Big Ten tournament to Minnesota, will play either UTEP or Lipscomb. Minnesota also was invited to the NIT and will play Wake Forest on Wednesday.
Louisville (18-12) will play in the first round Friday against the winner of Tuesday's opening game between Northern Arizona and Delaware State. Northern Arizona was the regular-season champion in the Big Sky conference and Delaware State was the Mid-Eastern Athletic champion, but both lost in their conference tournaments.
Cincinnati (19-12), which lost in the first round of the Big East tournament to Syracuse, will play Friday against either Georgia Southern or Charlotte.
Bearcats coach Andy Kennedy called the NCAA snub a disappointment and "an unfit ending for these kids."
The Missouri Valley Conference, which landed a record four teams in the NCAA tournament, will send two more to the NIT: Missouri State and Creighton. Both got No. 2 seeds.