The nonexistence of certain tight spherical designs
The nonexistence of certain tight spherical designs
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DOI：
10.1090/s1061-0022-05-00868-x
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发表时间：
2005-06
影响因子：
0.8
通讯作者：
E. Bannai;A. Munemasa;B. Venkov
中科院分区：
文献类型：
--
作者：
E. Bannai;A. Munemasa;B. Venkov
在本文中，在某些情况下，紧密的球形设计不存在。 ，2。在论文中，存在在整数m的某种算术条件下排除的存在，由无限的M = 4值满足。 - 设计可能存在于n = 3d2-4中，并且存在仅在d = 2，3中已知。在论文中，存在在d的某种算术条件下排除在d上，这是由无限的许多值所满足的。 d，包括d = 4。此外，d = 5显示了不存在的事实，即5个设计的m上的算术条件和7个设计的d上的d = 5，分别由M和D的无限值满足了M和D的无限值，在Y.-F中显示的附录。
In this paper, the nonexistence of tight spherical designs is shown in some cases left open to date. Tight spherical 5-designs may exist in dimension n = (2m + 1)2 − 2, and the existence is known only for m = 1, 2. In the paper, the existence is ruled out under a certain arithmetic condition on the integer m, satisfied by infinitely many values of m, including m = 4. Also, nonexistence is shown for m = 3. Tight spherical 7-designs may exist in dimension n = 3d2 − 4, and the existence is known only for d = 2, 3. In the paper, the existence is ruled out under a certain arithmetic condition on d, satisfied by infinitely many values of d, including d = 4. Also, nonexistence is shown for d = 5. The fact that the arithmetic conditions on m for 5-designs and on d for 7-designs are satisfied by infinitely many values of m and d, respectively, is shown in the Appendix written by Y.-F. S. Pétermann. §