IMPROVED BOUNDS ON SIZES OF GENERALIZED CAPS IN AG(n,q)

摘要

An m-general set in AG(n, q) is a set of points such that any subset of size m is in general position. A 3-general set is often called a capset. In this paper, we study the maximum size of an m-general set in AG(n, q), significantly improving previous results. When m = 4 and q = 2, we give a precise estimate, solving a problem raised by Bennett.