2026/07/22 by Sunanda Bagchi, Bhaskar Bagchi
Mathematics · #math.CO #msc:05B05 #msc:05B25 #msc:05B30
arxiv created 2026/08/02 · arxiv updated 2026/08/04
In this paper we prove that whenever a projective plane of odd order n contains an oval, it may be used to construct a triple array with n + 1 rows, n.n columns and n(n + 1) symbols. In particular, for any odd prime power s, we use the projective plane over the field of order s to construct an explicitly given (s + 1) times s.s triple array on s(s + 1) symbols. This is only the third infinite series of triple arrays (up to transposition) to be found. Our construction proves a recent conjecture of Gordeev and Ohman (2025) in the case of odd prime powers.