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

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

Offset: 0

Author

Dmitry Kamenetsky, Aug 04 2017

Keywords

• nonn
• more

Comments

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

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

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

Examples

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

References

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

Links

• Wikipedia, Disjunct Matrix

Crossrefs

Cf. A054961, A361928.