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Packing designs with block size 5 and indexes 8, 12, 16

โœ Scribed by Ahmed M Assaf; Nabil Shalaby


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
361 KB
Volume
59
Category
Article
ISSN
0097-3165

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Packing designs with block size 6 and in
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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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A (u, k, ,I) packing design of order u, block size k, and index I is a collection of k-element subsets, called blocks, of a u-set, V, such that every 2-subset of V occurs in at most A blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we solve

Balanced incomplete block designs with b
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## Abstract The necessary conditions for the existence of a balanced incomplete block design on ฯ…โ€‰โ‰ฅโ€‰__k__ points, with index ฮป and block size __k__, are that: For __k__โ€‰=โ€‰8, these conditions are known to be sufficient when ฮปโ€‰=โ€‰1, with 38 possible exceptions, the largest of which is ฯ…โ€‰=โ€‰3,753. For

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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 bloc

New results on GDDs, covering, packing a
โœ R. Julian R. Abel; Ahmed M. Assaf; Iliya Bluskov; Malcolm Greig; Nabil Shalaby ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 246 KB ๐Ÿ‘ 1 views

## Abstract This article looks at (5,ฮป) GDDs and (__v__,5,ฮป) pair packing and pair covering designs. For packing designs, we solve the (4__t__,5,3) class with two possible exceptions, solve 16 open cases with ฮป odd, and improve the maximum number of blocks in some (__v__, 5, ฮป) packings when __v__