Pedal Sets of Unitals in Projective Planes of Order 16

Abstract

In this article, we perform computer searches for pedal sets of all known unitals in the known planes of order 16. Special points of unitals having at least one special tangent are studied in detail. It is shown that unitals without special points exist. Open problems regarding the computational results presented in this study are discussed. A conjecture about the numbers of line types of an unital $U$ and its dual unital $U^\perp$ is formulated.

Keywords

• Pedal set
• Projective plane
• Unital

References

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