Maximal partial ovoids and maximal partial spreads in hermitian generalized quadrangles

✍ Scribed by K. Metsch; L. Storme

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 181 KB
• Volume: 16
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20146

✦ Synopsis

Abstract

Maximal partial ovoids and maximal partial spreads of the hermitian generalized quadrangles H(3,q^2^) and H(4,q^2^) are studied in great detail. We present improved lower bounds on the size of maximal partial ovoids and maximal partial spreads in the hermitian quadrangle H(4,q^2^). We also construct in H(3,q^2^), q=2^2__h__+1^, h≥ 1, maximal partial spreads of size smaller than the size q^2^+1 presently known. As a final result, we present a discrete spectrum result for the deficiencies of maximal partial spreads of H(4,q^2^) of small positive deficiency δ. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 101–116, 2008