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Jan 18, 2015 at 15:36 comment added Dima Pasechnik to generalise my example to another small $k$, take a the affine space of bigger dimension; in more generality, you can play with putting together different 2-designs with appropriate parameters.
Jan 18, 2015 at 15:30 comment added Dima Pasechnik generalising for arbitrary $k$ is hard, as optimal codes are in general not known.
Jan 18, 2015 at 14:16 comment added Jim How would this generalize to $k=15, 20$ or $30$? What if $n$ is odd. I have a feeling that the example in the edit is misleading because of its specific choice of $m=n/2$. It could just as well have been $m=2+n/5$. I'm interested in something that generalizes easily to arbitrary $n,k,m$.
Jan 16, 2015 at 21:12 history edited Dima Pasechnik CC BY-SA 3.0
answering a question from the comment
Jan 14, 2015 at 20:06 history answered Dima Pasechnik CC BY-SA 3.0