[seqfan] Sets of vectors over {0, 1}

Jens Voß jens at voss-ahrensburg.de
Thu Feb 13 21:54:46 CET 2014


There is a very interesting puzzle on math stackexchange at the moment:

In http://math.stackexchange.com/questions/667257, the author asks for 
the maximal size of a set S of n-tuples over {0, 1} such that all 
subsets of S have different sum vectors. (In fact, the original question 
asks for the value for n = 10.)

On contributor has reported to have come up with sets of sizes 4, 5, 7, 
9, 11, 13, 15, 17 for n = 3, 4, 5, 6, 7, 8, 9, 10; but it is not at all 
clear whether these values are in fact maximal.

As far as I can tell, the sequence is not in the database, or have I 
missed something? Can anyone confirm at least some of the sizes to be in 
fact maximal? I would expect a brute-force proof by calculation to be 
very hard, so maybe somebody can come up with an idea for a smarter 
approach?

Regards,
Jens


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