On resolvable designs S3(3;4,v)
Journal of Combinatorial Theory Series A
Design theory
New infinite families of simple 5-designs
Journal of Combinatorial Theory Series A
The existence of resolvable Steiner quadruple systems
Journal of Combinatorial Theory Series A
The existence of simple S3(3, 4, v)
Discrete Mathematics - Combinatorial designs: a tribute to Haim Hanani
The fundamental construction for 3-designs
Proceedings of the first Malta conference on Graphs and combinatorics
A construction for Steiner 3-designs
Journal of Combinatorial Theory Series A
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
An extension theorem for t-designs
Discrete Mathematics
A New Class of Designs Which Protect against Quantum Jumps
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Resolvable Steiner Quadruple Systems for the Last 23 Orders
SIAM Journal on Discrete Mathematics
Note: Simple abelian quadruple systems
Journal of Combinatorial Theory Series A
A construction of designs on n+1 points from multiply homogeneous permutation groups of degree n
Journal of Combinatorial Theory Series A
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In this paper we present a construction of 3-designs by using a 3-design with resolvability. The basic construction generalizes a well-known construction of simple 3-(v,4,3) designs by Jungnickel and Vanstone (1986). We investigate the conditions under which the designs obtained by the basic construction are simple. Many infinite families of simple 3-designs are presented, which are closely related to some known families by Iwasaki and Meixner (1995), Laue (2004) and van Tran (2000, 2001). On the other hand, the designs obtained by the basic construction possess various properties: A theory of constructing simple cyclic 3-(v,4,3) designs by Kohler (1981) can be readily rebuilt from the context of this paper. Moreover many infinite families of simple resolvable 3-designs are presented in comparison with some known families. We also show that for any prime power q and any odd integer n there exists a resolvable 3-(q^n+1,q+1,1) design. As far as the authors know, this is the first and the only known infinite family of resolvable t-(v,k,1) designs with t=3 and k=5. Those resolvable designs can again be used to obtain more infinite families of simple 3-designs through the basic construction.