There are two parts in this research. Firstly we solve most cases of the Lemmens-Seidel conjecture which was raised in 1973. The main tool here is to analyze the pillar decomposition for the upper bound of pillars. Secondly we verify that the current known constructions of equiangular sets in low dimensions are maximal (we call them saturated), then we use random number generators to produce new equiangular sets. We have constructed 56 equiangular lines in the 18-dimensional Euclidean space, which is the maximum known construction so far.
|Effective start/end date||2018/08/01 → 2019/07/31|
- Equiangular line sets
- Lemmens-Seidel conjecture
- pillar decomposition
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