Some Infinite Families of Large Sets of t-Designs

Some Infinite Families of Large Sets of t-Designs

A set of necessary conditions for existence of a large set of a t-design, LS ( (v−t k−t ) /n; t, k, v ) , is n| (v−i k−i ) for i = 0, 1, · · · , t. We show that these conditions are sufficient for n = 3, t = 2, 3, or 4, and k ≤ 8.

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, ...

New t-designs and large sets of t-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 ...