TY - JOUR

T1 - Packing designs with block size 6 and index 5

AU - Assaf, Ahmed M.

AU - Hartman, Alan

AU - Shalaby, N.

PY - 1992/5/27

Y1 - 1992/5/27

N2 - A (v, k{cyrillic}, λ) packing design of order v, block size k{cyrillic} and index λ is a collection of k{cyrillic}-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most λ blocks. The packing problem is to determine the maximum number of blocks in a packing design. The only previous work on the packing problem with k{cyrillic}=6 concerns itself with the cases where the maximum packing design is in fact a balanced incomplete block design. In this paper we solve the packing problem with k{cyrillic}=6 and λ=5 and all positive integers v with the possible exceptions of v=41, 47, 53, 59, 62, 71.

AB - A (v, k{cyrillic}, λ) packing design of order v, block size k{cyrillic} and index λ is a collection of k{cyrillic}-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most λ blocks. The packing problem is to determine the maximum number of blocks in a packing design. The only previous work on the packing problem with k{cyrillic}=6 concerns itself with the cases where the maximum packing design is in fact a balanced incomplete block design. In this paper we solve the packing problem with k{cyrillic}=6 and λ=5 and all positive integers v with the possible exceptions of v=41, 47, 53, 59, 62, 71.

UR - http://www.scopus.com/inward/record.url?scp=44049115658&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(92)90262-E

DO - 10.1016/0012-365X(92)90262-E

M3 - Article

AN - SCOPUS:44049115658

SN - 0012-365X

VL - 103

SP - 121

EP - 128

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -