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A234943 Array read by antidiagonals: T(i,j) = size of optimal difference triangle set M(i,j).

%I A234943 #23 Oct 17 2022 01:45:36
%S A234943 1,2,3,3,7,3,4,10,13,11,5,12,19,22,17,6,15,24,32,34,25,7,19,30,41,49,
%T A234943 51,34,8,22,36,51,64,72,70,44,9,24,42,60,79,94,100,94,55,10,27,48,71
%N A234943 Array read by antidiagonals: T(i,j) = size of optimal difference triangle set M(i,j).
%C A234943 An (n,k) difference triangle set is a set of n blocks of k integers such that the difference sets of the blocks are all disjoint. The "scope" of such a set is defined to be the maximal element, if all blocks are translated such that their least elements are all 0. T(n,k) lists the minimal scope for which an (n,k) difference triangle set exists. - _Charlie Neder_, Jun 14 2019
%D A234943 CRC Handbook of Combinatorial Designs, 1996, p. 315. (But beware errors!)
%H A234943 Yeow Meng Chee and Charles J. Colbourn, <a href="https://arxiv.org/abs/0712.2553">Constructions for Difference Triangle Sets</a>, arXiv:0712.2553 [cs.IT], 2007.
%H A234943 J. B. Shearer, <a href="https://web.archive.org/web/20180228224432/http://www.research.ibm.com/people/s/shearer/dtsopt.html">Difference Triangle Sets: Known optimal solutions</a>.
%H A234943 J. B. Shearer, <a href="https://web.archive.org/web/20171118235702/http://www.research.ibm.com/people/s/shearer/dtslb.html">Difference Triangle Sets: Discoverers</a>.
%e A234943 Array begins:
%e A234943 j\i|   1   2   3  4  5  6  7  8  9  10  11  12  13  14  15
%e A234943 ---+-----------------------------------------------------------------
%e A234943 1  |   1   2   3  4  5  6  7  8  9  10  11  12  13  14  15  (A000027)
%e A234943 2  |   3   7  10 12 15 19 22 24 27  31  34  36  39  43  46  (A013574)
%e A234943 3  |   6  13  19 24 30 36 42 48 54  60  66  72  78  84  90  (A013575)
%e A234943 4  |  11  22  32 41 51 60 71 80 91 100 111 120 131 140 151  (A013576)
%e A234943 5  |  17  34  49 64 79  (A013577)
%e A234943 6  |  25  51  72 94
%e A234943 7  |  34  70 100
%e A234943 8  |  44  94
%e A234943 9  |  55 121
%e A234943 10 |  72
%e A234943 11 |  85
%e A234943 12 | 106
%e A234943 13 | 127
%e A234943 14 | 151
%e A234943 15 | 177
%e A234943   A003022 A010896 A010898
%e A234943        A010895 A010897 A010899
%Y A234943 Rows and columns give A000027, A013574, A013575, A013576, A013577; A003022, A010895, A010896, A010897, A010898, A010899.
%Y A234943 For the number of different optimal triangle difference sets see the corresponding array in A234947.
%K A234943 nonn,tabl,more
%O A234943 1,2
%A A234943 _N. J. A. Sloane_, Jan 08 2014