Disjoint sets in projective planes of small order

Authors : Mustafa GEZEK

Pages : 803-814

Doi:10.31801/cfsuasmas.1194816

View : 29 | Download : 54

Publication Date : 2023-09-30

Article Type : Research Paper

Abstract :In this paper, results of a computer search for disjoint sets associated with maximal arcs and unitals in projective planes of order 16, and disjoint sets associated with unitals in projective planes of orders 9 and 25 are reported. It is shown that the number of pairs of disjoint unitals in planes of order 9 is exactly four, and new pairs and triples of disjoint degree 4 maximal arcs are shown to exist in some of the planes of order 16. New bounds on the number of 104-sets of type insert ignore into journalissuearticles values(4, 8); and 156-sets of type insert ignore into journalissuearticles values(8, 12); are achieved. A combinatorial method for finding new maximal arcs, new unitals, and new v-sets of type insert ignore into journalissuearticles values(m, n); is introduced. All disjoint sets found in this study are explicitly listed.
Keywords : Disjoint set, maximal arc, unital