The commission, which included former players (Grant Hill, David Robinson), former coaches, university presidents, the heads of the Association of American Universities and U.S.A. Basketball, and others, called on the N.C.A.A. to establish a new system for summer basketball, so central to the recruitment process, that could diminish the influence of the three main apparel companies. Adidas, Nike and Under Armour sponsor not only summer basketball but also most of the college teams that high school prospects aspire to play for.

Specifically, the commission envisioned allowing coaches as soon as next year to attend only N.C.A.A.-administered regional events during the crucial July evaluation period. It was not clear what role the three main sneaker companies would or would not have at those events. Each of them currently sponsors gigantic events in July that are unmissable for top prospects and coaches.

Prosecutors in the Southern District of New York have said that an Adidas executive and several others with ties to the sneaker giant were central to schemes to bribe players’ families and college basketball coaches to coax top prospects to commit to colleges that Adidas sponsored, like Louisville, Miami and Kansas, and later sign with Adidas. Narratives outlined by prosecutors strongly suggest that similar behavior is conducted in the name of Adidas’s rivals.

“The corruption we observed in college basketball has its roots in youth basketball,” Ms. Rice said in her statement.

In a statement, Adidas said it “welcomes the commission’s recommendations and will continue to work with the N.C.A.A. and other stakeholders in a collaborative and constructive manner.”

The commission suggested allowing players to have limited contact with agents, starting in high school, to help make decisions about the N.B.A. And it proposed permitting players who declare for the N.B.A. draft but are not selected to return to college. It also recommended increasing the severity of penalties for teams and coaches who violate rules, to five-year postseason bans for teams and lifetime suspensions for coaches. In addition, it said people outside the organization should be involved with the penalties process and serve on the N.C.A.A.’s board.