Maximum Size Binary Matroids with no AG(3, 2)-Minor are Graphic

We prove that the maximum size of a simple binary matroid of rank r ≥ 5 with no AG(3, 2)-minor is (r+1 2 ) and characterize those matroids achieving this bound. When r ≥ 6, the graphic matroid M(Kr+1) is the unique matroid meeting the bound, but there are a handful of matroids of lower ranks meeting or exceeding this bound. In addition, we determine the size function for nongraphic simple binary matroids with no AG(3, 2)-minor and characterize the matroids of maximum size for each rank.