There are 2834 spreads of lines in PG(3,8)

2014/04/07 by Brendan D. McKay, Gordon F. Royle, Gordon Royle +2
Engineering · Mathematics · Medicine · #Metastasis and carcinoma case studies #graph theory and CDMA systems #math.CO #msc:51E23

paper · pdf · doi:10.48550/arxiv.1404.1643

arxiv created 2014/04/07 · arxiv updated 2014/04/08

Abstract

2834 inequivalent spreads under the group PΓL(4,8). Therefore there are the same number of translation planes of order 64 with kernel containing GF(8), and we describe various properties of these planes. Each portion of the search was performed at least twice with independently-written software, and the results checked for internal consistency by computation of the numbers of spreads rooted at a line not in the spread, thus enhancing confidence in the correctness of the search.

Related

• A genealogy of the translation planes of order 25
• A computer search of maximal partial spreads in PG(3,q)
• A new class of maximal partial spreads in PG(4,q)
• New results on maximal partial line spreads in PG(5,q)
• A geometric characterisation of Desarguesian spreads