New t-designs and large sets of t-designs

Abstract

Recent results in the search for simple t-designs and large sets of t-designs are reported. Many new parameter sets of simple t-designs on up to 40 points and t ⩾ 7 are given. The tool used is a program DISCRETA, developed by the authors, which applies the method of Kramer-Mesner (Discrete Math. 15 (1976) 263–296) where an automorphism group of the desired designs is prescribed. In several cases Tran van Trung's (Arch. Math. 47 (1986) 187–192) and Alltop's (J. Combin. Theory A 18 (1975) 177–186) construction yield further results from those found by computer. By computer search we also constructed new large sets of t-designs, which enable via a theorem by Ajoodani-Namini (J. Combin Theory A 76 (1996) 139–144) the construction of infinite families of large sets of t-designs.