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Sep 24, 2013 at 21:11 comment added Aaron Meyerowitz An issue for this being the correct value is how disjoint the "radius $k$" sets can be. For example in the case $n=9$ the string $111000111$ can be reduced to $111111$ and to $111000$ and to $110011$, half the members of the six element covering set.
Sep 24, 2013 at 13:50 comment added Lucia I think your answer is essentially the same as Yury's nice answer from yesterday. Note that his $2^{0.08}$ is approximately your $1.058$. Yury suggested plausibly that this might be the right answer.
Sep 24, 2013 at 10:47 history answered Brendan McKay CC BY-SA 3.0