On KM-Arcs in Small Desarguesian Planes

Peter Vandendriessche

Abstract


In this paper we study the existence problem for KM-arcs in small Desarguesian planes. We establish a full classification of KM$_{q,t}$-arcs for $q\le 32$, up to projective equivalence. We also construct a KM$_{64,4}$-arc; as $t=4$ was the only value for which the existence of a KM$_{64,t}$-arc was unknown, this fully settles the existence problem for $q\le 64$.

Keywords


Desarguesian projective plane; KM-arcs; $(q+t,t)$-Arcs of type $(0,2,t)$

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