On k-sets of class \([0,q/2-1,q/2,q/2+1,q]\) in a plane of even order q
A set K of k points in a projective plane is said to be of class \([m_ 1,m_ 2,...,m_ s],\) \(0\leq m_ 1<m_ 2<...<m_ s\leq q+1\) (where q is the order of the plane) if for each line \(\ell\) of the plane, \(| K\cap \ell |\) is one of the numbers \(m_ i.\) The paper is a bit more general than the title indicates. All k-sets of type \((m_ 1,m_ 2)\) are listed; much information is given on k-sets of type \([m_ 1,m_ 2,m_ 3]\) and \([m_ 1,m_ 2,m_ 3,m_ 4]\). The final result is that when \(q\geq 8\) there is no set of the type indicated in the title with a unique O-secant. The point sets which show up are such things as affine planes, dual affine planes, ovals, dual ovals or one of the above with a few points added or deleted.
scientific article; zbMATH DE number 3940119
scientific article