There seems to be some confusion out there about what picks the Nets have, what picks they've given up and what picks they must swap ... and under what circumstances. So here are the details...
The Nets have first round picks in 2015, 2017, 2019 and 2020, the furthest year a pick can be traded, and have none from other teams. The picks in 2015 and 2017 can be swapped --to the Hawks in 2015 and the Celtics in 2017. BUT the Nets will have a pick in those two years, either their own or the other teams'.
They traded their first round picks --unprotected-- in 2014, 2016 and 2018 to the Celtics. Unless they can acquire a first round pick in the years they traded to the Celtics, they won't be able to trade their first round picks in 2015 and 2017 under the NBA's Stepien Rule. That rule prohibits teams from trading first round picks in successive years. Their 2015 and 2017 picks must be swapped ONLY if they're higher than the Hawks (2015) and Celtics (2017) picks.
So if the Nets finish with a higher pick (after the lottery) in 2015, their pick goes to Atlanta and the Hawks' pick goes to the Nets. If the Hawks have a higher pick, the Nets first round pick stays in Brooklyn. So, in either case, the Nets will have a first round pick. The same is true in 2017, with the Celtics pick. Nets get a higher pick, they give it up to Boston and use the Celtics' pick. If not, the pick is their own.
They have four second round picks in the seven drafts between 2014 through 2020 but one is heavily protected and is likely to wind up with Clippers.. They could pick one up from the Celtics in 2017, but there are protections favorable to Boston on that one. Here are the details on the second round picks:
--On Draft Night in 2011, the Nets sent their second round pick in 2014 and their 2010 first round pick (Jujaun Johnson) to Boston for MarShon Brooks.
--In the 2011 Mehmet Okur trade, the Nets sent their second round pick in 2015 to Utah for .
--In 2012, the Nets agreed to swap second round picks in 2016 with the Clippers in return for Reggie Evans. The Clippers have the option to swap picks with the Nets if the Clippers pick is #31-55. The Nets can still trade the pick if the other team is willing to assume the risk.
--In the 2012 Joe Johnson trade, the Nets sent their second round in 2017 pick to Atlanta. It wasn't included in the original deal but the league required it because of a CBA technicality.
--In 2018, the Nets have their own second round pick.
--In 2019, the Nets have their own second round pick.
They have also acquired the rights to another pick, but both it's of limited value, a so-called "paper pick." If Boston exercises its right to swap its 2017 first round pick for Brooklyn's 2017 first round pick, then Boston will convey its 2017 second round pick to Brooklyn protected for selections #31 through #45. If Boston's pick falls with that range, the first half of the second round, the Celtics will keep it and the Nets get nothing.