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- W3208890662 abstract "Let the kissing number $K(d)$ be the maximum number of non-overlapping unit balls in $mathbb R^d$ that can touch a given unit ball. Determining or estimating the number $K(d)$ has a long history, with the value of $K(3)$ being the subject of a famous discussion between Gregory and Newton in 1694. We prove that, as the dimension $d$ goes to infinity, $$ K(d)ge (1+o(1)){frac{sqrt{3pi}}{4sqrt2}},logfrac{3}{2}cdot d^{3/2}cdot Big(frac{2}{sqrt{3}}Big)^{d}, $$ thus improving the previously best known bound of Jenssen, Joos and Perkins by a factor of $log(3/2)/log(9/8)+o(1)=3.442...$. Our proof is based on the novel approach from Jenssen, Joos and Perkins that uses the hard core sphere model of an appropriate fugacity. Similar constant-factor improvements in lower bounds are also obtained for general spherical codes, as well as for the expected density of random sphere packings in the Euclidean space $mathbb R^d$." @default.
- W3208890662 created "2021-11-08" @default.
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- W3208890662 date "2021-11-01" @default.
- W3208890662 modified "2023-09-26" @default.
- W3208890662 title "New lower bounds on kissing numbers and spherical codes in high dimensions." @default.
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