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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
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 17:01 EDT 2021. Contains 343050 sequences. (Running on oeis4.)