Root cases of large sets of t-designs

Root cases of large sets of t-designs

A large set of t-(v, k, λ) designs of size N , denoted by LS[N ](t, k, v), is a partition of all k-subsets of a v-set into N disjoint t-(v, k, λ) designs, where N = ( v−t k−t ) /λ. A set of trivial necessary conditions for the existence of an LS[N ](t, k, v) is N ∣

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, ...