Resolvable balanced incomplete block designs with block size 8
type: Item
instance of: scholarly article
title: Resolvable balanced incomplete block designs with block size 8
zbMATH Open document ID: 0883.05013
DOI: 10.1023/A:1008224620163
author: Malcolm Greig
author: R. Julian R. Abel
published in: Designs, Codes and Cryptography
publication date: 1998-02-22T00:00:00Z
review text: A balanced incomplete block design (BIBD) \(D\) is a collection \(B\) of subsets (blocks) taken from a finite set \(V\) of \(v\) elements with the properties: (1) every pair of distinct elements of \(V\) is contained in precisely \(\lambda\) blocks of \(B\), and (2) every block contains exactly \(k\) elements. We denote such a design as a \((v,k,\lambda)\)-BIBD. A \((v,k,\lambda)\)-BIBD is said to be resolvable if the blocks can be partitioned in classes \(R_1,R_2,\dots,R_r\) (resolution classes) where \(r=\lambda (v-1)/(k-1)\) such that each element of \(D\) is contained in precisely one block of each class. The resolution classes \(R_1,R_2,\dots,R_r\) form a resolution of \(D\). A necessary condition for the existence of a resolvable \((v,8,1)\)-BIBD is that \(v\equiv 8\pmod{56}\). With the possible exception of 66 values of \(v\), this condition is shown to be sufficient. The largest exceptional value of \(v\) is 24480.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1028922
zbMATH Keywords: balanced incomplete block design
zbMATH Keywords: resolution classes
zbMATH Keywords: resolution
reviewed by: Esther R. Lamken
MaRDI profile type: Publication
full work available at URL: a:1008224620163
OpenAlex ID: W2051507061
description: scientific article; zbMATH DE number 1028922