Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*)

Abstract A (k,n) arc in the finite projective PG(2,q) is defined to be the set K which is composed of k points such that there is a line passes through n points but no line can pass through more than n points. A (k,n) arc is called complete if there is no (k+1,n) arc containing it. In this research we have constructed and classified all the projectively distinct (k,5) arcs for k = 7, 8, 9 in the projective planes PG(2,9). We proved that (k,5) arcs are not complete in the projective plane PG(2, 9) for 5 k 25. We contructed and classified the (13,5) arcs in the projective plane PG(2,9) where all of these arcs containing a conic by using a computer program .