On the incompleteness of (k,n)-arcs in Desarguesian planes of order q where n|q

We investigate the completeness of an ( nq – q + n – , n)-arc in the Desarguesian plane of order q where n divides q. It is shown that such arcs are incomplete for 0 <0.381n=" and=" for=" q="3n" they=" are=" incomplete=" for=" 0="> = 0 and, hence, we improve the upper bound on the maximum size of such a ( k, n)-arc.