Some t-designs are minimal (t + 1)-coverings

Some Indecomposable t-Designs

The existence of large sets of 5-(14,6,3) designs is in doubt. There are five simple 5-(14,6,6) designs known in the literature. In this note, by the use of a computer program, we show that all of these designs are indecomposable and therefore they do not lead to large sets of 5(14,6,3) designs. Moreover, they provide the first counterexamples for a conjecture on disjoint t-designs which states...

New coverings of t-sets with (t + 1)-sets

The minimum number of k-subsets out of a v-set such that each t-set is contained in at least one k-set is denoted by C (v; k; t). In this paper, a computer search for nding good such covering designs, leading to new upper bounds on C (v; k; t), is considered. The search is facilitated by predetermining automorphisms of desired covering designs. A stochastic heuristic search (embedded in the gen...

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, ...

Some new families of simple t-designs

Applying some methods of construction on existing i-designs, we obtain some infinite families of new simple designs. We give a table which contains many new simple designs in small cases. The main method which is called the union method, involves taking the union of every two blocks in a given design. We also combine this method with some other well known ones. Some of the new designs obtained ...