Smallest defining sets of designs associated with PG(d, 2)
نویسنده
چکیده
For d 2:: 2, let Dd be the symmetric block design formed from the points and hyperplanes of the projective space PG(d, 2). Let 3d equal the number of blocks in a smallest defining set of Dd . The known results 32 = 3 and S3 = 9 are reviewed and it is shown that 34 = 24 and 52 :::; 35 :::; 55. If J-Ld = 3d/ (2d+ 1 1) is the proportion of blocks in a smallest defining set of Dd, then J-L2 = 3/7, J-L3 = 9/15 and J-L4 = 24/31. The main result of this paper is that J-Ld -+ 1 as d -+ 00.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 16 شماره
صفحات -
تاریخ انتشار 1997