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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.

%I A066701 #14 Feb 02 2020 21:27:50
%S A066701 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,
%T A066701 1,1,1,58,1,40,1,20,1,1,1,1,2
%N 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.
%C A066701 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).
%D A066701 CRC Handbook of Combinatorial Designs, 1996, p. 263.
%D A066701 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.
%H A066701 D. Applegate, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205303">On asymmetric coverings and covering numbers</a>, J. Comb. Des. 11 (2003), 218-228.
%H A066701 D. Gordon, <a href="http://www.dmgordon.org/cover">La Jolla Repository of Coverings</a>
%H A066701 K. J. Nurmela and Patric R. J. Östergård, <a href="http://www.tcs.hut.fi/old/papers/tp1.ps.Z">New coverings of t-sets with (t+1)-sets</a>, J. Combinat. Designs, 7 (1999), 217-226.
%H A066701 K. J. Nurmela and Patric R. J. Östergård, <a href="http://www.tcs.hut.fi/old/papers/table3.html">New coverings of t-sets with (t+1)-sets (appendix)</a>, J. Combinat. Designs, 7 (1999), 217-226.
%H A066701 <a href="/index/Cor#covnum">Index entries for covering numbers</a>
%H A066701 <a href="/index/St#Steiner">Index entries for sequences related to Steiner systems</a>
%Y A066701 Cf. A066010. A030129 gives entries in second column in the cases when a Steiner triple system exists.
%Y A066701 A051390 gives entries in 3rd column in the cases when a Steiner quadruple system exists.
%K A066701 nonn,nice,tabl
%O A066701 2,18
%A A066701 _N. J. A. Sloane_, Jan 11 2002