# An investigation of the tangent splash of a subplane of $$\mathrm{PG}(2,q^3)$$PG(2,q3)

@article{Barwick2015AnIO, title={An investigation of the tangent splash of a subplane of \$\$\mathrm\{PG\}(2,q^3)\$\$PG(2,q3)}, author={Susan G. Barwick and Wen-Ai Jackson}, journal={Designs, Codes and Cryptography}, year={2015}, volume={76}, pages={451-468} }

In $$\mathrm{PG}(2,q^3)$$PG(2,q3), let $$\pi $$π be a subplane of order $$q$$q that is tangent to $$\ell _\infty $$ℓ∞. The tangent splash of $$\pi $$π is defined to be the set of $$q^2+1$$q2+1 points on $$\ell _\infty $$ℓ∞ that lie on a line of $$\pi $$π. This article investigates properties of the tangent splash. We show that all tangent splashes are projectively equivalent, investigate sublines contained in a tangent splash, and consider the structure of a tangent splash in the Bruck–Bose…

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Let $\pi$ be an order-$q$-subplane of $PG(2,q^3)$ that is exterior to $\ell_\infty$. The exterior splash of $\pi$ is the set of $q^2+q+1$ points on $\ell_\infty$ that lie on an extended line of…

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