New t-designs and large sets of t-designs

A Betten
1999 Discrete Mathematics  
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 Yran van Trung's (Arch. Math. 47 (1986) 187-192) and Alltop's (J. Combin. Theory A 18 (1975)
more » ... ) 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.
doi:10.1016/s0012-365x(98)00226-x fatcat:v4a3i5w4o5bvtpbvzdepedo4ti