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.Comment: Revised version. To appear in SIAM Journal on Discrete Mathematic