New values for mr (2, 29)‎ and tr (2, 29)‎ in PG (2, 29)‎

الملخص EN

In this paper we find the neare complete (n, r)-arcs of the maximum value for mr(2,29)-arc when 2 ≤ r ≤ 28 .

Also, we find the nearest minimum size of complete tr (2, 29)-arcs when 2 ≤ r ≤ 28, as well as we set some open questions concerning for non-existence of complete (n, r)-arcs.

All this done by a computer program, noteworthy that there is no results published till now when 8 ≤ r ≤ 28 for mr(2,29) and there are no results published till now for tr(2,29) when 3 ≤ r ≤ 28 in PG(2,29) according to the knowledge of the authors.