Re: [math-fun] poisoned wine bottles: more-perfect-union codes

Here's a better code abstraction of the poisoned bottle problem: "more perfect union" code on n symbols: Codewords are subsets of the n symbols with the property that if A and B are distinct codewords as are C and D, then A u B = C u D implies A = C, B = D or A = D, B = C. As before, let M(n) be the maximum number of codewords in a code on n symbols. I've checked that M(n) = n+1 for n < 6. These are the "Speciner codes", given by the empty set and all the singletons (11 as opposed to just 10 codes in the original problem). But already for n = 6 there is an improvement. The following code shows M(6) >= 8: {{4}, {5}, {1, 3}, {2, 6}, {1, 2, 5}, {1, 4, 6}, {2, 3, 4}, {3, 5, 6}} Any ideas on finding good bounds on M(10)? -Veit