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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