Disjoint sets in projective planes of small order

Year 2023, Volume: 72 Issue: 3, 803 - 814, 30.09.2023

Mustafa Gezek

https://doi.org/10.31801/cfsuasmas.1194816

Cited By: 1

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 (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.

Keywords

Disjoint set, maximal arc, unital

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