zbMATH — the first resource for mathematics

The existence of simple \(6\text{-}(14,7,4)\) designs. (English) Zbl 0647.05013
Summary: A cyclic \(5\text{-}(13,6,4)\) design is constructed and is extended to a simple \(6\text{-}(14,7,4)\) design via a theorem of W. O. Alltop [ J. Comb. Theory, Ser. A 18, 177–186 (1975; Zbl 0297.05028)]. This design is the smallest possible nontrivial simple 6-design that can exist. Both have full automorphism group cyclic of order 13.

05B05 Combinatorial aspects of block designs
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
Full Text: DOI
[1] Alltop, W.O, Extending t-designs, J. combin. theory ser. A, 18, 177-186, (1975) · Zbl 0297.05028
[2] Kramer, E.S, Some t-designs for t⩾4 and t=17, 18, (), 443-460
[3] Kramer, E.S; Leavitt, D.W; Magliveras, S.S, Construction procedures for t-designs and the existence of new simple 6-designs, (), 247-274
[4] Kramer, E.S; Mesner, D.M, t-designs on hypergraphs, Discrete math., 15, 263-296, (1976) · Zbl 0362.05049
[5] Kramer, E.S; Magliveras, S.S; Mesner, D.M, t-designs from the large Mathieu groups, Discrete math., 36, 171-189, (1981) · Zbl 0471.05011
[6] Kreher, D.L; Radziszowski, S.P, Finding simple t-designs by basis reduction, (), Winnipeg, Manitoba, Canada · Zbl 0616.05022
[7] Lagarias, J.C; Odlyzko, A.M, Solving low-density subset sum problem, J. assoc. comput. Mach., 32, No. 1, 229-246, (1985) · Zbl 0632.94007
[8] Lenstra, A.K; Lenstra, H.W; Lovász, L, Factoring polynomials with rational coefficients, Math. ann., 261, 515-534, (1982) · Zbl 0488.12001
[9] Magliveras, S.S; Leavitt, D.W, Simple 6-(33, 8, 36) designs from PγL2(32), (), 337-352
[10] Radziszowski, S.P; Kreher, D.L, Solving subset-sum problem with the L3 algorithm, (1986), to appear
[11] Sims, C.C, Computational methods in the study of permutation groups, () · Zbl 0215.10002
[12] Wielandt, H, Finite permutation groups, (1964), Academic Press New York/London · Zbl 0138.02501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.