New Lower Bounds for Cap Sets

A cap set is a subset of F-3(n) with no solutions to x + y + z = 0 other than when x = y = z. In this paper, we provide a new lower bound on the size of a maximal cap set. Building on a construction of Edel, we use improved computational methods and new theoretical ideas to show that, for large enough n, there is always a cap set in F-3(n) of size at least 2.218(n).