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We explore explicit virtual resolutions, as introduced by Berkesch, Erman, and Smith, for ideals of sets of points in P 1 × P 1 . Specifically, we describe a virtual resolution for a sufficiently general set of points X in P 1 × P 1 that only depends on |X|. We also improve an existence result of Berkesch, Erman, and Smith in the special case of points in P 1 × P 1 ; more precisely, we give an effective bound for their construction that gives a virtual resolution of length two for any set of points in P 1 × P 1 .