Large \(k\)-arcs in inversive planes of odd order (Q1818910)

In the inversive plane \({\mathcal M}(q)\) over a finite field \(\text{GF}(q)\), a \(k\)-arc is a set of \(k\) points no four of which lie on the same circle. The author constructs a maximal \({1\over 3}(q+5)\)-arc in \({\mathcal M}(q)\), where \(q\equiv 1\pmod 6\) and \(q\geq 73\) or \(q=49\). This is the first known infinite family of large \(k\)-arcs in finite inversive planes.