國立清華大學 數學系

A set of lines in Rⁿ passing through the origin is called equiangular if any two lines of them form  the same angle. Searching the maximum size of equiangular lines in Rⁿ is one of the classical problem in discrete geometry. We offer the alternative semidefinite programming formula for spherical codes in contrast to Bachoc-Vallentin. The alternative formula would be simpler for implementation. Furthermore, we use the four point semidefinite programming method symbolically to improve the upper bounds on the size of equiangular lines in Rⁿ. Our results improve the bounds for infinitely many dimensions.