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Dear GAP-Forum,

You might be interested in the web-page

http://www.maths.qmw.ac.uk/~leonard/partialspreads/

where I report on new classifications obtained using GAP and GRAPE in

the study of partial spreads in finite projective spaces (a *partial

spread* is a set of (projective) lines, no pair of which have a

(projective) point in common).

I include GAP/GRAPE log-files with the web-page, which detail the

computations. These should be of interest both to finite geometers and

to those seeking extended examples of the use of GRAPE.

Highlights include the complete classification of maximal partial

spreads in PG(3,4) and the discovery and classification of maximal

partial spreads of size 45 in PG(3,7) invariant under a group of order

5 (until quite recently it was conjectured that a largest maximal

partial spread of PG(3,q) which did not partition the points of PG(3,q)

would have size at most q^2-q+2).

Hope this is of interest.

-Leonard Soicher

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