Large sets of subspace 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 ...

New t-designs and large sets of t-designs

Large sets of disjoint t-designs

[u this paper, we show how the basis reduction algorithm of Kreher and Radziszowski can be used to construct large sets of disjoint designs with specified automorphisms. In particular, we construct a (3,4,23;4)large set which rise to an infinite family of large sets of 4-desiglls via a result of Teirlinck [6].

Some small large sets of t-designs

Some new large sets of t-designs

By constructing a new large set of 4-(13,5,3) designs, and using a recursive construction described recently by Qiu-rong Wu, we produce an infinite family of large sets and as a byproduct an infinite family of new 4-designs. Similarly, we construct a new large set of 3-(13,4,2) designs, and obtain an infinite family of large sets of 3-designs. We also include a large set of 2-(14,4,6) designs, ...