What is cap set?

A cap set is a set of numbers in which no two numbers add up to a third number in the same set. It is named after mathematician Paul Erdős, who first studied it in 1956. The cap set problem has applications in coding theory and cryptography. The best-known result in this area is due to Alexei Borodin, who showed that the size of a cap set in a group of prime order p is at most (3/4) p^(1/2). However, it is not known whether this bound is sharp, and finding the maximum size of a cap set remains an open problem in combinatorics.