New large sets oft-designs

Abstract

Abstact: We introduce generalizations of earlier direct methods for constructing large sets of t-designs. These are based on assembling systematically orbits of t-homogeneous permutation groups in their induced actions on k-subsets. By means of these techniques and the known recursive methods we construct an extensive number of new large sets, including new infinite families. In particular, a new series of LS[3](2(2 + m), 8·3m − 2, 16·3m − 3) is obtained. This also provides the smallest known ν for a t-(ν, k, λ) design when t ≥ 16. We present our results compactly for ν ≤ 61, in tables derived from Pascal's triangle modulo appropriate primes. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 40–59, 2001