A finite projective plane of order n, with n > 0, is a collection of n
2+ n + 1 lines and n2
+ n + 1 points such that
1. every line contains n + 1 points,
2. every point is on n + 1 lines,
3. any two distinct lines intersect at exactly one point, and
4. any two distinct points lie on exactly one line.
It is known that a plane of order n exists if n is a prime power. The first value of n which is not a prime power is 6. Tarry  proved in 1900 that a pair of orthogonal latin squares of order 6 does not exist, which by Bose's 1938 result  implies that a projective plane of order 6 does not exist.