Probabilistic existence of large sets of designs

Probabilistic Existence of Large Sets of Designs

A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been introduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain conditions, a randomly chosen structure has the required properties of a t(n, k, λ) combinatorial design with tiny, yet positive, probability. Herein, we strengthen both ...

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...

On 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...

Some results on the existence of large sets of t-designs

A set of trivial necessary conditions for the existence of a large set of t-designs, LS[N ](t, k, v), is N ∣

New t-designs and large sets of t-designs