A Few More Large Sets of t-Designs
نویسندگان
چکیده
We construct several new large sets of t-designs that are invariant under Frobenius groups, and discuss their consequences. These large sets give rise to further new large sets by means of known recursive constructions including an infinite family of large sets of 3− (v, 4, λ) designs. c © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 293–308, 1998
منابع مشابه
On the existence of large sets of t-designs of prime sizes1
In this paper, we employ the known recursive construction methods to obtain some new existence results for large sets of t-designs of prime sizes. We also present a new recursive construction which leads to more comprehensive theorems on large sets of sizes two and three. As an application, we show that for infinitely many values of block size, the trivial necessary conditions for the existence...
متن کاملLARGE SETS OF t−DESIGNS FROM GROUPS
This paper addresses questions related to the existence and construction of large sets of t-(v, k, λ) designs. It contains material from my talk in the Combinatorial Designs Conference in honor of Alex Rosa’s 70th birthday, which took place in beautiful Bratislava, in July, 2007. Naturally, only a small number of “highlight” topics could be included, and for the most part these involve the use ...
متن کاملOn the Existence of Large Sets of t-designs of Prime Sizes
In this paper, we use the known recursive construction methods to obtain some new existence results for large sets of t-designs of prime sizes. We also present a new recursive construction which leads to more comprehensive theorems on large sets of sizes two and three. As an application, we show that for infinitely many values of block size, the trivial necessary conditions for the existence of...
متن کاملOn Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs
A defining set of a t-(v, k, λ) design is a partial design which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given t-design. The complete list of minimal defining sets of...
متن کاملGenealogy of t-designs
Abstract Recent years have seen a dramatic increase in existence results for tdesigns with large t, i.e. t ≥ 5. Designs are now known to exist for several thousand parameter sets, mostly constructed by the method of orbiting under a group. This note is a contribution to the classification of these designs by parameters. We take an abstract look at admissible parameter sets in general. We introd...
متن کامل