Covering t-sets with (t + 2)-sets

Discrete Applied Mathematics

Volumn 95, Issue 1-3, 1999, Pages 425-437

  Nurmela, Kari J ^a   Östergård, Patric R J ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Automorphism group; Combinatorial optimization; Covering design; Tabu search

Indexed keywords

EID: 0041777709     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00090-6     Document Type: Article

References (25)

1. J.A. Bate, G.H.J. van Rees, Some results on N(4, 6, 10), N(4, 6, 11), and related coverings, Congr. Numer. 48 (1985) 25-45.
2. R. Belić, personal communication.
3. I.D. Bluskov, H. Hämäläinen, New upper bounds on the minimum size of covering designs, J. Combin. Des. 6 (1998) 21-41.
4. E.D. Boyer, D.L. Kreher, S.P. Radziszowski, J. Zou, A. Sidorenko, On (n, 5, 3)-Turán systems, Ars Combin. 37 (1994) 1-19.
5. A.E. Brouwer, A few new constant-weight codes, IEEE Trans. Inform. Theory 26 (1980) 366.
6. L.G. Chouinard II, R. Jajcay, S.S. Magliveras, Finite groups and designs, in: C.J. Colbourn, J.H. Dinitz (Eds.), The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, 1996, pp. 587-615.
7. R.H.F. Denniston, Some new 5-designs, Bull. London Math. Soc. 8 (1976) 263-267.
8. P.B. Gibbons, Computational methods in design theory, in: C.J. Colbourn, J.H. Dinitz (Eds.), The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, 1996, pp. 718-740.
9. F. Glover, Tabu search - part I, ORSA J. Comput. 1 (1989) 190-206.
10. ∼xm3dg/cover.html (electronic).
11. D.M. Gordon, O. Patashnik, G. Kuperberg, New constructions for covering designs, J. Combin. Des. 3 (1995) 269-284.
12. J.D. Horton, R.C. Mullin, R.G. Stanton, Minimal coverings of pairs by quadruples, Congr. Numer. 3 (1971) 495-516.
13. E.S. Kramer, D.M. Mesner, t-designs on hypergraphs, Discrete Math. 15 (1976) 263-296.
14. D.L. Kreher, S.P. Radziszowski, The existence of simple 6-(14, 7, 4) designs, J. Combin. Theory Ser. A 43 (1986) 237-243.
15. W.H. Mills, On the covering of pairs by quadruples I, J. Combin. Theory Ser. A 13 (1972) 55-78.
16. W.H. Mills, On the covering of pairs by quadruples II, J. Combin. Theory Ser. A 15 (1973) 138-166.
17. W.H. Mills, R.C. Mullin, Coverings and packings, in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory: A Collection of Surveys, Wiley, New York, 1992, pp. 371-399.
18. K.J. Nurmela, M.K. Kaikkonen, P.R.J. Östergård, New constant weight codes from linear permutation groups, IEEE Trans. Inform. Theory 43 (1997) 1623-1630.
19. K.J. Nurmela, P.R.J. Östergård, Upper bounds for covering designs by simulated annealing, Congr. Numer. 96 (1993) 93-111.
20. K.J. Nurmela, P.R.J. Östergård, New coverings of t-sets with (t + 1)-sets, J. Combin. Des., to appear.
21. J. Schönheim, On coverings, Pacific. J. Math. 14 (1964) 1405-1411.
22. R.G. Stanton, J.A. Bate, A computer search for B-coverings, in: R.W. Robinson, G.W. Southern, W.D. Wallis (Eds.), Combinatorial Mathematics VII, Lecture Notes in Computer Science, vol. 829, Springer-Verlag, New York, 1980, pp. 37-50.
23. D.R. Stinson, Coverings, in: C.J. Colbourn, J.H. Dinitz (Eds.), The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, 1996, pp. 260-265.
24. P. Turán, Eine Extremalaufgabe aus der Graphentheorie, Mat. Fiz. Lapok 48 (1941) 436-452 (in Hungarian).
25. E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg 12 (1938) 256-264.