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

0,2

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

References

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

Links

Table of n, a(n) for n=0..12.

Wikipedia, Disjunct Matrix

Example

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

Crossrefs

Cf. A054961.

Sequence in context: A043318 A044915 A161951 * A191431 A191430 A011760

Adjacent sequences: A290489 A290490 A290491 * A290493 A290494 A290495

Keyword

nonn,more

Author

Dmitry Kamenetsky, Aug 04 2017

Status

approved