A066701 Triangle giving number of nonisomorphic minimal covering designs with parameters (n, k, k-1) (designs achieving the covering number C(n,k,k-1) given in A066010), for n >= 2, 2 <= k <= n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 6, 1, 1, 1, 1, 1, 77, 3, 2, 1, 1, 1, 1, 58, 1, 40, 1, 20, 1, 1, 1, 1, 2

Offset

2,18

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. This sequence says how many different solutions there are for C(n,k,k-1).

References

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

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=2..48.

D. Applegate, E. M. Rains and N. J. A. Sloane, On asymmetric coverings and covering numbers, 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.

Index entries for covering numbers

Index entries for sequences related to Steiner systems

Crossrefs

Cf. A066010. A030129 gives entries in second column in the cases when a Steiner triple system exists.

A051390 gives entries in 3rd column in the cases when a Steiner quadruple system exists.

Sequence in context: A193349 A380587 A053231 * A046563 A046591 A361236

Adjacent sequences: A066698 A066699 A066700 * A066702 A066703 A066704

Keyword

nonn,nice,tabl

Author

N. J. A. Sloane, Jan 11 2002

Status

approved