Unitals in projective planes of order 16


Abstract: In this study, we perform computer searches for unitals in planes of order 16. The number of known nonisomorphic unitals in these planes is improved to be 261. Some data related to 2-$(65,5,1)$ designs associated with unitals are given. New lower bounds on the number of unital designs in projective planes of order 16 and 2-$(65,5,1)$ designs are established. The computations show that thirty-nine unitals can be embedded in two or more nonisomorphic projective planes of order 16. Fifteen new connections between planes of order 16 (based on unitals) are found. All unitals found by the algorithms used in this study are explicitly listed.

Keywords: Unital, projective plane, Steiner design, graph isomorphism, orbits, automorphism group

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