Geodesic
Sets of Disjoint Lines in PG(3, q)
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 273-280

Voir la notice de l'article provenant de la source Cambridge University Press

Let ∑ be a projective space PG(3, q) of dimension 3 and finite order q. Then ∑ contains (q + 1)(q2 + 1) points and an equal number of planes, and (q2 + 1) (q2 + q + 1) lines. It will be convenient to consider lines and planes as sets of points and to treat the incidence relation as set inclusion. Each plane contains q2 + q + 1 points and an equal number of lines. Each line contains q + 1 points and is contained in an equal number of planes. Each point is contained in q2 + q + 1 planes and an equal number of lines.A spread of lines of ∑ is a set of q2 + 1 lines of ∑ which are pairwise disjoint, or skew; it can also be defined as a set of lines such that each point (or each plane) is incident with exactly one of the lines. 
Mesner, Dale M. Sets of Disjoint Lines in PG(3, q). Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 273-280. doi: 10.4153/CJM-1967-019-5
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