(k,n;f)–arcs of type (1,n) in PG(2,q), with q leq 8

In this paper we discussed the existence of ( k, n; f ) – arcs of type ( 1, n ) in the projective plane of order q≤8; with Im( f ) = { 0, 1, ω } and ω∈{2,3,…,n-1}, that different from G. Raguso and L. Rella ( k, n; f ) – arcs [12] and we deduced that there are no such ( k, n; f ) – arcs of type (1, n) with Im( f ) = { 0, 1, ω } in PG(2, q) for all ω∈{2,3,…,n-1}, q≤7 and for all n satisfy (n-1)|q. But when q=8, we have only (19, 9; f ) – arc of type (1, 9), with Im( f ) = { 0, 1, 4 }, such that the points of weight 4 form an oval and the points of weight 1 are the points of some 0 – secant of this oval.