Pappus configurations in the Hall plane

Abstract

In this paper, we investigate Pappus configurations in the finite affine Hall plane. In particular, we show that for any two lines ${\ell }_1,{\ell }_2$ and for any triple of points on ${\ell }_1$ there is a triple of points on ${\ell }_2$ that are contained in a Pappus configuration, thus improving on the results of [F. Lazebnik and L. Leshock. On Pappus configurations in Hall planes. Des. Codes Cryptogr. 90 (2022), 1203--1219.].