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Existence results for near resolvable designs
Author(s) -
Furino Steven
Publication year - 1995
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/jcd.3180030204
Subject(s) - mathematics , combinatorics , block (permutation group theory) , integer (computer science) , class (philosophy) , point (geometry) , set (abstract data type) , block design , discrete mathematics , geometry , computer science , artificial intelligence , programming language
A near resolvable design, NRB ( v, k ), is a balanced incomplete block design whose block set can be partitioned into v classes such that each class contains every point of the design but one, and each point is missing from exactly one class. The necessary conditions for the existence of near resolvable designs are v ≡ 1 mod k and λ = k − 1. These necessary conditions have been shown to be sufficient for k ϵ {2,3,4} and almost always sufficient for k ϵ {5,6}. We are able to show that there exists an integer n 0 ( k ) so that NRB ( v,k ) exist for all v > n 0 ( k ) and v ≡ 1 mod k. Using some new direct constructions we show that there are many k for which it is easy to compute an explicit bound on n 0 ( k ). These direct constructions also allow us to build previously unknown NRB ( v ,5) and NRB ( v ,6). © 1995 John Wiley & Sons, Inc.