Singer 8-arcs of Mathon type in PG(2, 27)

In [3] De Clerck, De Winter and Maes counted the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2, 2), h 6= 7 and prime. In this article we will show that in PG(2, 2) a special class of Mathon maximal arcs of degree 8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a detailed description of these arcs, and then count the total number of non-isomorphic Mathon maximal arcs of degree 8. Finally we show that the special arcs found in PG(2, 2) extend to two infinite families of Mathon arcs of degree 8 in PG(2, 2), k odd and divisible by 7, while maintaining the nice property of admitting a Singer group.