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A question of Ahlswede and Katona: known lower bounds on $\beta(d,n)$?

(0) Preliminaries: (a) factors: above you should change the factors $\frac{1}{4}$ on the rhs of your equations (4) and (5) to $\frac{1}{2}$ (Kündgens distance is half the distance of Ahlswede/Katona …
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