Note on GMW designs
The classical difference sets with the classical parameters \[ ((q^n-1)/(q-1), (q^{n-1}-1)/(q-1), (q^{n-2}-1)/(q-1)) \] are the Singer difference sets (\(q\) is a prime power). The corresponding symmetric design is the classical point-hyperplane design of the \(n-1\)-dimensional projective space. For arbitrary prime powers \(q\), only one more general construction of difference sets with the classical parameters is known (GMW construction, see \textit{B. Gordon, W. H. Mills} and \textit{L. R. Welch} [Some new difference sets, Can. J. Math. 14, 614-625 (1962; Zbl 0111.24201)]). It is an old question to decide whether inequivalent GMW difference sets yield nonisomorphic designs. In this short but highly nontrivial paper, Kantor shows that isomorphism implies equivalence. The proof uses group theory, and therefore seems to be inappropriate for proving this (geometric) result (in the words of the author, ``using a cannon to kill an ant'').
scientific article; zbMATH DE number 1567134