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2834 inequivalent spreads under the group $\mathrm{P}\Gamma\mathrm{L}(4,8)$.Therefore there are the same number of translation planes of order 64 withkernel containing $\mathrm{GF}(8)$, and we describe various properties of theseplanes.  Each portion of the search was performed at least twice withindependently-written software, and the results checked for internalconsistency by computation of the numbers of spreads rooted at a line not inthe spread, thus enhancing confidence in the correctness of the search.

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