# 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}
}
• Published 22 March 2013
• Mathematics
• Designs, Codes and Cryptography
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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