The D 4 Root System Is Not Universally Optimal
نویسندگان
چکیده
We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the D4 root system.
منابع مشابه
. M G ] 9 S ep 2 00 8 THE D 4 ROOT SYSTEM IS NOT UNIVERSALLY OPTIMAL
We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a constr...
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عنوان ژورنال:
- Experimental Mathematics
دوره 16 شماره
صفحات -
تاریخ انتشار 2007