Constructions of optimal packing designs

✍ Scribed by Jianxing Yin; Ahmed M. Assaf

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 195 KB
• Volume: 6
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/(sici)1520-6610(1998)6:4<245::aid-jcd3>3.0.co;2-f

✦ Synopsis

Let v and k be positive integers. A (v, k, 1)-packing design is an ordered pair (V, B B B) where V is a v-set and B B B is a collection of k-subsets of V (called blocks) such that every 2-subset of V occurs in at most one block of B B B. The packing problem is mainly to determine the packing number P (k, v), that is, the maximum number of blocks in such a packing design. It is well known

) where x denotes the greatest integer y such that y ≤ x. A (v, k, 1)-packing design having J(k, v) blocks is said to be optimal. In this article, we develop some general constructions to obtain optimal packing designs. As an application, we show that P (5, v) = J(5, v) if v ≡ 7, 11 or 15 (mod 20), with the exception of v ∈ {11, 15} and the possible exception of v