The maximum and the minimum size of complete (n,3)-arcs in PG(2,16)
Daniele Bartoli, Stefano Marcugini, Fernanda Pambianco
TL;DR
This paper determines the maximum and minimum sizes of complete (n,3)-arcs in PG(2,16), providing exact bounds and partial classification, advancing understanding of geometric configurations in finite projective planes.
Contribution
It precisely establishes the extremal sizes of complete (n,3)-arcs in PG(2,16) and offers a partial classification of these configurations.
Findings
Maximum size of complete (n,3)-arcs is 28
Minimum size of complete (n,3)-arcs is 15
Partial classification of extremal arcs in PG(2,16)
Abstract
In this work we solve the packing problem for complete (n,3)-arcs in PG(2,16), determining that the maximum size is 28 and the minimum size is 15. We also performed a partial classification of the extremal size of complete (n,3)-arcs in PG(2,16).
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · graph theory and CDMA systems