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 knownnonisomorphic unitals in these planes is improved to be 261. Some data related to 2-(65, 5, 1) designs associated withunitals 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 nonisomorphicprojective planes of order 16. Fifteen new connections between planes of order 16 (based on unitals) are found. Allunitals found by the algorithms used in this study are explicitly listed.