Extending Large Sets oft-Designs

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, ...

LARGE 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 ...