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On the classification of linear spaces of order 11

✍ Scribed by Ch. Pietsch

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 427 KB
Volume: 3
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180030305

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✦ Synopsis

A linear space of order n is a pair (V, a), where V is a finite set of n elements and B is a set of subsets of V such that each 2-subset of V is contained in exactly one element of B. The exact number of nonisomorphic linear spaces was known up to order 10. Betten and Braun [l] found that there exist at least 232,923 uonisomorphic linear spaces of order 11. We used a generalization of Ivanov's algorithm for the enumeration of block designs in order to construct all 232,929 linear spaces of order 11. The method used will be described and some data concerning line types, line lengths, and orders of automorphism groups is listed.

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