#### Vol. 4, No. 1, 2006

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About maximal partial 2-spreads in $\mathrm{PG}(3m-1,q)$

### Szabolcs L. Fancsali and Péter Sziklai

Vol. 4 (2006), No. 1, 89–102
DOI: 10.2140/iig.2006.4.89
##### Abstract

In this article we construct maximal partial 2-spreads in $PG\left(8,q\right)$ of deficiency $\delta =\left(k-1\right)\cdot {q}^{2}$, where $k\le {q}^{2}+q+1$ and $\delta =k\cdot {q}^{2}+l\cdot \left({q}^{2}-1\right)+1$, where $k+l\le {q}^{2}$ and $\delta =\left(k+1\right)\cdot {q}^{2}+l\cdot \left({q}^{2}-1\right)+m\cdot \left({q}^{2}-2\right)+1$, where $k+l+m\le {q}^{2}$. Using these results, we also construct maximal partial 2-spreads in $PG\left(3m-1,q\right)$ of various deficiencies for $m\ge 4$.