Geodesic
Sets of type $(a,b)$ from subgroups of $\Gamma L (1, p^R)$
Journal of Algebraic Combinatorics, Tome 13 (2001) no. 1, pp. 67-76.

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Summary: In this paper $k$-sets of type $( a, b)$ with respect to hyperplanes are constructed in finite projective spaces using powers of Singer cycles. These are then used to construct further examples of sets of type $( a, b)$ using various disjoint sets. The parameters of the associated strongly regular graphs are also calculated. The construction technique is then related to work of Foulser and Kallaher classifying rank three subgroups of $AGammaL(1, p ^{R})$. It is shown that the sets of type $( a, b)$ arising from the Foulser and Kallaher construction in the case of projective spaces are isomorphic to some of those constructed in the present paper.
Keywords: $k$-set of type $( a$, b)$$, singer cycle, strongly regular graph 
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     title = {Sets of type $(a,b)$ from subgroups of $\Gamma L (1, p^R)$},
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Hamilton, Nicholas; Penttila, Tim. Sets of type $(a,b)$ from subgroups of $\Gamma L (1, p^R)$. Journal of Algebraic Combinatorics, Tome 13 (2001) no. 1, pp. 67-76. http://geodesic.mathdoc.fr/item/JAC_2001__13_1_a2/