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A290492 Maximal number of binary vectors of length n such that the unions (or bitwise ORs) of any 3 distinct vectors are all distinct. 0

%I

%S 1,2,3,4,5,6,7,8,9,10,11,12,14

%N Maximal number of binary vectors of length n such that the unions (or bitwise ORs) of any 3 distinct vectors are all distinct.

%C Maximal number of subsets of an n-set such that the unions of any 3 distinct subsets are all distinct.

%C The concatenation of these vectors produces a 3-separable matrix.

%C 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 Background: D.-Z. Du and F. K. Hwang, Combinatorial Group Testing and Its Applications, World Scientific, 2nd ed., 2000; see Chap. 7.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Disjunct_matrix">Disjunct Matrix</a>

%e Here is a solution for n=12: {100000001100 000001010001 100101100000 010000110100 000110000101 011100000000 001000101001 000000000000 101010010000 001001000110 000100011010 000010100010 110000000011 010011001000}.

%Y Cf. A054961.

%K nonn,more

%O 0,2

%A _Dmitry Kamenetsky_, Aug 04 2017

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Last modified May 16 17:22 EDT 2021. Contains 343949 sequences. (Running on oeis4.)