论文标题
线性编程范围用于覆盖球形设计半径
Linear programming bounds for covering radius of spherical designs
论文作者
论文摘要
我们应用多项式技术（线性编程），以在球形设计的覆盖半径上获得其尺寸，强度和基数的功能。在内部产品方面，我们改善了由于Fazekas和Levenshtein引起的下限，并提出了新的上限。我们对下限的方法涉及某些签名的度量，其相应的正交多项式序列是正面的，直到一定（适当）程度。上限基于几何观察和或多或少的标准线性编程技术。
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower bounds due to Fazekas and Levenshtein and propose new upper bounds. Our approach to the lower bounds involves certain signed measures whose corresponding series of orthogonal polynomials are positive definite up to a certain (appropriate) degree. Upper bounds are based on a geometric observation and more or less standard linear programming techniques.
