Nonexistence of a (783, 69, 6)-difference set (Q1377824)

This paper provides a one page proof that there is no (783, 69, 6)-difference set in the group \(Z^3_3 \times Z_{29}\). This excludes one of the last four open cases of abelian \((v,k, \lambda)\)-difference sets with \(k\leq 100\); see \textit{D. Jungnickel} and \textit{A. Pott} [Difference sets: Abelian, in C. J. Colbourn and J. H. Dinitz, eds., The CRC handbook of combinatorial designs. CRC Press Series on Discrete Mathematics and its Applications. 297-307 (1996; Zbl 0851.05024)].