A011983 Covering numbers C(n,5,4).

1, 5, 9, 20, 30, 51, 66, 113

Offset

5,2

Comments

C(v,k,t) is the smallest number of k-subsets of an n-set such that every t-subset is contained in at least one of the k-subsets.

a(13) <= 157.

References

CRC Handbook of Combinatorial Designs, 1996, p. 263.

D. De Caen, D. L. Kreher, S. P. Radziszowski, and W. H. Mills, On the covering of t-sets with (t+1)-sets: C(9,5,4) and C(10,6,5). Discrete Math. 92 (1991), no. 1-3, 65-77.

W. H. Mills and R. C. Mullin, Coverings and packings, pp. 371-399 of Jeffrey H. Dinitz and D. R. Stinson, editors, Contemporary Design Theory, Wiley, 1992.

Links

Table of n, a(n) for n=5..12.

D. Applegate, E. M. Rains and N. J. A. Sloane, On asymmetric coverings and covering numbers, arXiv:math/0205303 [math.CO], 2002; J. Comb. Des. 11 (2003), 218-228.

D. Gordon, La Jolla Repository of Coverings.

K. J. Nurmela and Patric R. J. Östergård, New coverings of t-sets with (t+1)-sets, J. Combinat. Designs, 7 (1999), 217-226.

K. J. Nurmela and Patric R. J. Östergård, New coverings of t-sets with (t+1)-sets (appendix), J. Combinat. Designs, 7 (1999), 217-226.

Wikipedia, Covering design.

Index entries for covering numbers.

Crossrefs

Cf. A066009. A column of A066010.

Sequence in context: A309731 A253951 A102172 * A087940 A340360 A323110

Adjacent sequences: A011980 A011981 A011982 * A011984 A011985 A011986

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Status

approved