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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 575.05008

**Autor: ** Erdös, Paul; Fowler, Joel C.; Sós, Vera T.; Wilson, Richard M.

**Title: ** On 2-designs. (In English)

**Source: ** J. Comb. Theory, Ser. A 38, 131-142 (1985).

**Review: ** The set of b for which there exists a linear space with v points and b lines is studied very sharply, particularly for large v and for v of the form n^{2}+n+1. Interesting is an extremal case: if v = n^{2}+n+1, b = n^{2}2n+1 the space is obtained from a projective plane replacing one of its lines with a near pencil or a projective plane. Conjectures and problems are given too.

**Reviewer: ** G.Ferrero

**Classif.: ** * 05B05 Block designs (combinatorics)

05B20 (0,1)-matrices (combinatorics)

51A05 General theory of linear incidence geometry

51E30 Other finite incidence structures

**Keywords: ** linear space; projective plane

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