English

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

Combinatorics 2014-04-08 v1

Abstract

2834 inequivalent spreads under the group PΓL(4,8)\mathrm{P}\Gamma\mathrm{L}(4,8). Therefore there are the same number of translation planes of order 64 with kernel containing GF(8)\mathrm{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.

Keywords

Cite

@article{arxiv.1404.1643,
  title  = {There are 2834 spreads of lines in PG(3,8)},
  author = {Brendan D. McKay and Gordon F. Royle},
  journal= {arXiv preprint arXiv:1404.1643},
  year   = {2014}
}