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A240119 Schoenheim lower bound L(n,6,3).

%I A240119 #20 Jan 26 2019 14:27:44
%S A240119 1,4,4,6,7,11,14,18,19,30,32,37,42,57,64,70,77,104,112,121,130,167,
%T A240119 178,194,205,248,267,286,301,362,378,401,425,494,520,547,574,667,697,
%U A240119 728,759,870,904,948,984,1105,1153,1202,1242,1394,1438,1492,1547,1711
%N A240119 Schoenheim lower bound L(n,6,3).
%H A240119 Colin Barker, <a href="/A240119/b240119.txt">Table of n, a(n) for n = 6..1000</a>
%H A240119 D. Gordon, G. Kuperberg and O. Patashnik, <a href="http://arxiv.org/abs/math/9502238">New constructions for covering designs</a>, arXiv:math/9502238 [math.CO], 1995.
%t A240119 schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
%t A240119 Table[schoenheim[n, 6, 3], {n, 6, 100}] (* _Jean-François Alcover_, Jan 26 2019, from PARI *)
%o A240119 (PARI) schoenheim(n, k, t) = {
%o A240119   my(lb = 1);
%o A240119   n += 1-t; k += 1-t;
%o A240119   while(t>0,
%o A240119     lb = ceil((lb*n)/k);
%o A240119     t--; n++; k++
%o A240119   );
%o A240119   lb
%o A240119 }
%o A240119 s=[]; for(n=6, 100, s=concat(s, schoenheim(n, 6, 3))); s
%Y A240119 Cf. A240115, A240116, A240117, A240118.
%Y A240119 Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.
%K A240119 nonn
%O A240119 6,2
%A A240119 _Colin Barker_, Apr 01 2014