## Innovations in Incidence Geometry

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

#### Abstract

In this article we construct maximal partial 2-spreads in $PG ( 8 , q )$ of deficiency $δ = ( k − 1 ) ⋅ q 2$, where $k ≤ q 2 + q + 1$ and $δ = k ⋅ q 2 + l ⋅ ( q 2 − 1 ) + 1$, where $k + l ≤ q 2$ and $δ = ( k + 1 ) ⋅ q 2 + l ⋅ ( q 2 − 1 ) + m ⋅ ( q 2 − 2 ) + 1$, where $k + l + m ≤ q 2$. Using these results, we also construct maximal partial 2-spreads in $PG ( 3 m − 1 , q )$ of various deficiencies for $m ≥ 4$.

#### Article information

Source
Innov. Incidence Geom., Volume 4 (2006), 89-102.

Dates
Received: 21 December 2005
Accepted: 5 March 2007
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323226

Digital Object Identifier
doi:10.2140/iig.2006.4.89

Mathematical Reviews number (MathSciNet)
MR2334647

Zentralblatt MATH identifier
1130.51004

Subjects
Primary: 51E23: Spreads and packing problems

Keywords
Fancsali, Szabolcs L.; Sziklai, Péter. About maximal partial 2-spreads in $\mathrm{PG}(3m-1,q)$. Innov. Incidence Geom. 4 (2006), 89--102. doi:10.2140/iig.2006.4.89. https://projecteuclid.org/euclid.iig/1551323226
• A. Gács and T. Szőnyi, On maximal partial spreads in $\PG(n,q)$, Des. Codes Cryptogr. 29 (2003), no. 1-3, 123–129.