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There is no (46, 6, 1) block design *
Author(s) -
Houghten S.K.,
Thiel L.H.,
Janssen J.,
Lam C.W.H.
Publication year - 2001
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/1520-6610(2001)9:1<60::aid-jcd5>3.0.co;2-w
Subject(s) - row , combinatorics , row and column spaces , mathematics , incidence matrix , column (typography) , block (permutation group theory) , matrix (chemical analysis) , block design , computer science , geometry , connection (principal bundle) , engineering , materials science , structural engineering , database , node (physics) , composite material
Abstact: In this paper we show that a (46, 6, 1) design does not exist. This result was obtained by a computer search. In the incidence matrix of such a design, there must exist a “c4” configuration—6 rows and 4 columns, in which each pair of columns intersect exactly once, in distinct rows. There can also exist a “c5” configuration with 10 rows and 5 columns, in which each pair of columns intersect exactly once, in distinct rows. Thus the search for (46, 6, 1) designs can be subdivided into two cases, the first of which assumes there is no “c5”, and the second of which assumes there is a “c5”. After completing the searches for both cases, we found no (46, 6, 1) design. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 60–71, 2001