No extendable biplane of order nine
type: Item
instance of: scholarly article
title: No extendable biplane of order nine
zbMATH Open document ID: 0662.05010
DOI: 10.1016/0097-3165(88)90025-8
author: Bhaskar Bagchi
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: A t-(v,k,\(\lambda)\) design is a v-set S provided with a collection of k- subsets of s, called blocks, such that any t-subset of S is contained in exactly \(\lambda\) blocks. Using coding theoretic arguments, the author proves the nonexistence of a 3-(57,12,2) design. Together with a result of \textit{P. J. Cameron} [J. Comb. Theory, Ser. A 14, 215-220 (1973; Zbl 0252.05010)] and the nonexistence of a 3-(112,12,1) design [\textit{C. W. H. Lam}, \textit{L. Thiel}, \textit{S. Swiercz}, and \textit{J. Mckay}, Discrete Math. 45, 319-321 (1983; Zbl 0574.05008)] this shows that the only extendable biplane is the one of order three.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 51E05
zbMATH DE Number: 4081570
zbMATH Keywords: symmetric design
zbMATH Keywords: t-(v,k,\(\lambda \) ) design
zbMATH Keywords: biplane
reviewed by: Luc Teirlinck
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90025-8
OpenAlex ID: W2029512250
cites work: Extending symmetric designs
cites work: Q3863891
cites work: Q3885773
cites work: Q3932736
cites work: The nonexistence of ovals in a projective plane of order 10
cites work: A New Family of Partially Balanced Incomplete Block Designs with Some Latin Square Design Properties
cites work: On the uniqueness of the Golay codes
cites work: Maximal arcs in designs
description: scientific article; zbMATH DE number 4081570