Construction Of Complete ( K,N )-Arcs In PG ( 2,8) FOR M < N

In this work, we construct complete (k,n)-arcs and we find some of them are maximum for some n, 2 < n < 8. if n = 2, where every arc which constructed by the equation of the conic called conic arc, and from it we constructs complete arcs and we prove it’s maximum by taking the union of two ,three and six conics , respectively. and then we show By adding the points of index zero for the (k6,6)-arc, (k7,7)-arc, respectively, we get a maximum complete (k8,8)-arc.