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Sets of disjoint lines in ${ m PG}(3,,q)$

1967
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Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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1. Spreads and partial spreads. Let S be a projective space PG(3, q) of dimension 3 and finite order q. Then 2 contains (q + l)(q 2 + 1) points and an equal number of planes, and (q 2 + 1) (q 2 + 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 q 2 + 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

doi:10.4153/cjm-1967-019-5
fatcat:2t3fqv3lljhlbb6zg5cfxhwsgy