This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A290492 #17 Nov 14 2024 08:23:11
%S A290492 1,2,3,4,5,6,7,8,9,10,11,12,14
%N A290492 Maximal number of binary vectors of length n such that the unions (or bitwise ORs) of any 3 distinct vectors are all distinct.
%C A290492 Maximal number of subsets of an n-set such that the unions of any 3 distinct subsets are all distinct.
%C A290492 The concatenation of these vectors produces a 3-separable matrix.
%C A290492 a(13) >= 15. Here is a candidate solution: {1100100010000 0100010000011 0001101000001 0000000011001 1010000100001 0010100001010 0101000101000 0001000000000 0110001000100 0000110000100 0000001100010 1001000000110 0000000110100 0011010010000 1000011001000}. - _Dmitry Kamenetsky_, Sep 07 2017
%D A290492 Background: D.-Z. Du and F. K. Hwang, Combinatorial Group Testing and Its Applications, World Scientific, 2nd ed., 2000; see Chap. 7.
%H A290492 Wikipedia, <a href="https://en.wikipedia.org/wiki/Disjunct_matrix">Disjunct Matrix</a>
%e A290492 Here is a solution for n=12: {100000001100 000001010001 100101100000 010000110100 000110000101 011100000000 001000101001 000000000000 101010010000 001001000110 000100011010 000010100010 110000000011 010011001000}.
%Y A290492 Cf. A054961, A361928.
%K A290492 nonn,more
%O A290492 0,2
%A A290492 _Dmitry Kamenetsky_, Aug 04 2017