✦ LIBER ✦

Existence of large sets of coverings with block size 3

✍ Scribed by L. Ji

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 84 KB
Volume: 14
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20077

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Two types of large sets of coverings were introduced by T. Etzion (J Combin Designs, 2(1994), 359–374). What is maximum number (denoted by λ(n,k)) of disjoint optimal (n,k,k − 1) coverings? What is the minimum number (denoted by µ(n,k)) of disjoint optimal (n,k,k − 1) coverings for which the union covers the space? For k = 3, the numbers µ(n,k) have been determined with an unsolved order n = 17, and the numbers λ(n,k) have also been determined with an unsolved infinite class n ≡ 5 (mod 6). The unsolved numbers λ(n,3) and µ(17,3) will be completed in this note. This solution is based on the existence of a class of partitionable candelabra systems. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 400–405, 2006

📜 SIMILAR VOLUMES

Existence of large sets of disjoint grou

Existence of large sets of disjoint group-divisible designs with block size three and type 2n41

✍ L. Ji 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 142 KB 👁 2 views

## Abstract Large sets of disjoint group‐divisible designs with block size three and type 2^__n__^4^1^ (denoted by __LS__ (2^__n__^4^1^)) were first studied by Schellenberg and Stinson and motivated by their connection with perfect threshold schemes. It is known that such large sets can exist only

Existence of HPMDs with block size five

✍ F. E. Bennett; Y. Chang; J. Yin; H. Zhang 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 194 KB

In this article, it is shown that the necessary condition for the existence of a holey perfect Mendelsohn design (HPMD) with block size 5 and type h n , namely, n ≥ 5 and n(n -1)h 2 ≡ 0 (mod 5), is also sufficient, except possibly for a few cases. The results of this article guarantee the analogous

Existence of directed GDDs with block si

Existence of directed GDDs with block size five

✍ F. E. Bennett; Nabil Shalaby; Jianxing Yin 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 393 KB 👁 1 views

In this article, we construct directed group divisible designs (DGDDs) with block size five, group-type h n , and index unity. The necessary conditions for the existence of such a DGDD are n ≥ 5, (n -1)h ≡ 0 (mod 2) and n(n -1)h 2 ≡ 0 (mod 10). It is shown that these necessary conditions are also su

Large sets of disjoint group-divisible d

Large sets of disjoint group-divisible designs with block size three and type 2n41

✍ H. Cao; J. Lei; L. Zhu 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB 👁 1 views

## Abstract Large sets of disjoint group‐divisible designs with block size three and type 2^__n__^4^1^ have been studied by Schellenberg, Chen, Lindner and Stinson. These large sets have applications in cryptography in the construction of perfect threshold schemes. It is known that such large sets

On the existence of mandatory representa

On the existence of mandatory representation designs with block sizes 3 and k

✍ Martin Grüttmüller 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 117 KB 👁 2 views

Further results on large sets of disjoin

Further results on large sets of disjoint group-divisible designs with block size three and type 2n41

✍ H. Cao; J. Lei; L. Zhu 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 137 KB 👁 2 views

## Abstract Large sets of disjoint group‐divisible designs with block size three and type 2^n^4^1^ were first studied by Schellenberg and Stinson because of their connection with perfect threshold schemes. It is known that such large sets can exist only for __n__ ≡0 (mod 3) and do exist for all odd