TY - JOUR

T1 - Saturated configuration and new large construction of equiangular lines

AU - Lin, Yen chi Roger

AU - Yu, Wei Hsuan

N1 - Funding Information:
The first author is partially supported by 107-2115-M-003-001 from Ministry of Science and Technology, Taiwan. Part of this work is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while the second author was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Point configurations in Geometry, Physics and Computer Science Program. Part of this work was done when the second author visited National Center for Theoretical Sciences (NCTS), Taiwan, in the summer of 2017. The authors are grateful to the support of NCTS. The authors wish to thank Prof. E. Bannai and Gary Greaves for their useful comments.
Funding Information:
The first author is partially supported by 107-2115-M-003-001 from Ministry of Science and Technology, Taiwan . Part of this work is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while the second author was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Point configurations in Geometry, Physics and Computer Science Program. Part of this work was done when the second author visited National Center for Theoretical Sciences (NCTS), Taiwan, in the summer of 2017. The authors are grateful to the support of NCTS. The authors wish to thank Prof. E. Bannai and Gary Greaves for their useful comments. Appendix A Below we include the SAGE code for generating an equiangular set of 248 lines in R 42 with angle 1/7, which is a subset of 344 equiangular lines in R 43 that comes from the strongly regular graph SRG ( 344 , 168 , 92 , 72 ) .
Publisher Copyright:
© 2019

PY - 2020/3/1

Y1 - 2020/3/1

N2 - A set of lines through the origin in Euclidean space is called equiangular when any pair of lines from the set intersects with each other at a common angle. We study the maximum size of equiangular lines in Euclidean space and use a graph theoretic approach to prove that all the currently known constructions for maximum equiangular lines in Rd cannot be added by any more lines to form a larger equiangular set of lines when d=14,16,17,18,19, and 20. We give new constructions of large equiangular lines which are 248 equiangular lines in R42, 200 equiangular lines in R41, 168 equiangular lines in R40, 152 equiangular lines in R39 with angle 1/7, and 56 equiangular lines in R18 with angle 1/5.

AB - A set of lines through the origin in Euclidean space is called equiangular when any pair of lines from the set intersects with each other at a common angle. We study the maximum size of equiangular lines in Euclidean space and use a graph theoretic approach to prove that all the currently known constructions for maximum equiangular lines in Rd cannot be added by any more lines to form a larger equiangular set of lines when d=14,16,17,18,19, and 20. We give new constructions of large equiangular lines which are 248 equiangular lines in R42, 200 equiangular lines in R41, 168 equiangular lines in R40, 152 equiangular lines in R39 with angle 1/7, and 56 equiangular lines in R18 with angle 1/5.

KW - Clique number

KW - Equiangular lines

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U2 - 10.1016/j.laa.2019.12.002

DO - 10.1016/j.laa.2019.12.002

M3 - Article

AN - SCOPUS:85075982299

SN - 0024-3795

VL - 588

SP - 272

EP - 281

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -