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On small packing and covering designs with block size 4

โœ Scribed by Alan Hartman

Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
325 KB
Volume
59
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

A packing (respectively covering) design of order v, block size k, and index ~ is a collection of k-element subsets, called blocks, of a v-set, V, such that every 2-subset of V occurs in at most (at least) 3. blocks. The packing (covering) problem is to determine the maximum (minimum) number of blocks in a packing (covering) design. Motivated by the recent work of Assaf [1] [2], we solve the outstanding packing and covering problems with block size 4.

๐Ÿ“œ SIMILAR VOLUMES

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A (v, K, A) packing design of order v, block size K and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most I blocks. The packing problem is to determine the maximum number of blocks in a packing design. The only previous work on

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## Abstract A Kirkman holey packing (resp. covering) design, denoted by KHPD(__g^u^__) (resp. KHCD(__g^u^__)), is a resolvable (__gu__, 3, 1) packing (resp. covering) design of pairs with __u__ disjoint holes of size __g__, which has the maximum (resp. minimum) possible number of parallel classes.