On a refinement of Craig’s lattices |
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| Authors: | André Luiz Flores,Trajano Pires da Nó brega Neto |
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| Affiliation: | a Departamento de Matemática, Universidade Federal de Alagoas, Av. Manoel Severino Barbosa, s/n, 57309-005 Arapiraca, AL, Brazilb Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-7720, USAc Departamento de Matemática, Universidade Estadual Paulista, Rua Cristóvão Colombo, 2265, 15054-000 São José do Rio Preto, SP, Brazild Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, Bloco 914, 60455-760 Fortaleza, CE, Brazil |
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| Abstract: | Let p be an odd prime. A family of (p−1)-dimensional over-lattices yielding new record packings for several values of p in the interval [149…3001] is presented. The result is obtained by modifying Craig’s construction and considering conveniently chosen Z-submodules of Q(ζ), where ζ is a primitive pth root of unity. For p≥59, it is shown that the center density of the (p−1)-dimensional lattice in the new family is at least twice the center density of the (p−1)-dimensional Craig lattice. |
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| Keywords: | 11H31 11R04 11R18 |
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