Matt Williams, a 6-5 guard who impressed the Heat with his three-point shooting during the NBA’s Summer League, signed with Miami on Monday, becoming the Heat’s 15th player under contract.

Williams, undrafted out of Central Florida, did not sign a two-way contract, according to a league source. But Williams and the Heat could decide before the season to make his deal a two-way deal if both sides agree to that.

Under the NBA’s new two-way contract rules, teams can retain rights to 17 players (up from 15 in past years), with the 16th and 17th players signed to two-way contracts and not eligible to play more than 45 days for an NBA team during that season. The rest of the time must be spent with the NBA team’s D-League affiliate.

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But Williams’ deal, at least for now, carries no such restrictions.

NBA teams can carry 17 players during the regular season, with two signed to those two-way contracts, and as many as 20 players before and during training camp.

Williams (on the left of the picture above) appeared in eight games with the Heat’s summer league teams in Orlando and Las Vegas, starting six of them, and averaged 9.9 points and 2.6 rebounds while shooting 38 percent from the field and 39 percent from three-point range.

He started all six games in Las Vegas with Miami and shot 45 percent from three-point range, leading the team in three-point field goals made four times, including a 5-of-8 performance on threes against Washington on July 10 and a 6-of-9 effort on threes against Memphis on July 15.

Williams, 6-5, finished as UCF’s all-time leader in three-point field goals made (274) and became the 18th player in program history to score at least 1,000 points.

He appeared in 36 games (all starts) as a senior and averaged 15.1 points, 4.3 rebounds, 1.9 assists and 36.5 minutes while shooting 39.1 percent from the field, 38.4 percent from three-point range and 81.1 percent from the foul line.

He set the single-season school and conference records for three-point field goals made (126) and set the Knights’ single-game three-point field goals made record after connecting on 11 against USF on January 17.

In my piece here last week, one scout explained why Williams was the Heat’s Summer League prospect (aside from Bam Adebayo, Okaro White and A.J. Hammons) who was best equipped to be an NBA player.

The Heat still can sign players to minimum contracts and also has a $4.3 million exception, which Pat Riley has suggested Miami will hold on to for now.

The Heat tonight signed former Michigan point guard Derrick Walton Jr. to a two-way contract. Here are details on him.

I’ve been out for several days for a pre-Dolphins training camp break but will have several posts on Tuesday, so check back then.