Switching sets in 𝑃𝐺(3,𝑞)

Bruen, A.; Silverman, R.

doi:10.1090/S0002-9939-1974-0333946-8

Switching sets in $\textrm {PG}(3, q)$
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by A. Bruen and R. Silverman

Proc. Amer. Math. Soc. 43 (1974), 176-180

DOI: https://doi.org/10.1090/S0002-9939-1974-0333946-8

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Abstract:

In this note, we are mainly concerned with partial spreads $U,V$ of $PG(3,q)$ which cover the same points and have no line in common. Setting $|U| = |V| = t$, we show that if $t > q + 1$ then $t \geqq \max (q + 2,2q - 2)$. Certain applications of this result to (0, 1) matrices and to translation planes are then discussed.

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