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We extend previous results by Frankl, Frankl and Watanabe, and Piga and Sch\\\"ulke by proving that for all integers $d$ and $m$ with $d\\geq m\\geq 1$, we have $\\alpha(2^d-m)=\\frac{2^{d+1}-m}{d+1}$. 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We extend previous results by Frankl, Frankl and Watanabe, and Piga and Sch\\\"ulke by proving that for all integers $d$ and $m$ with $d\\geq m\\geq 1$, we have $\\alpha(2^d-m)=\\frac{2^{d+1}-m}{d+1}$. 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