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 (4, 8) and 156-sets of type (8, 12) are achieved. A combinatorial method for finding new maximal arcs, new unitals, and new v-sets of type (m, n) is introduced. All disjoint sets found in this study are explicitly listed.
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 30 Eylül 2023 |
Gönderilme Tarihi | 26 Ekim 2022 |
Kabul Tarihi | 8 Mart 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 72 Sayı: 3 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
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