### Abstract

Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as good as Zink’s bound; i.e. λ(BBGS/F

_{q3}) ≥ 2(q^{2 }- 1)/(q + 2). In this paper, the exact value of λ(BBGS/F_{q3}) is computed. We also settle a question stated by Ihara.Original language | English |
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Title of host publication | Proceedings of the International Conference on Arithmetic, Geometry, Cryptography and Coding theory (2015) |

Number of pages | 17 |

Publisher | American Mathematical Society |

Publication date | 2017 |

Publication status | Published - 2017 |

Event | 15th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory - Marseille, France Duration: 18 May 2015 → 22 May 2015 Conference number: 15 http://scientific-events.weebly.com/1193.html |

### Conference

Conference | 15th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory |
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Number | 15 |

Country | France |

City | Marseille |

Period | 18/05/2015 → 22/05/2015 |

Internet address |

Series | Contemporary Mathematics |
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Volume | 686 |

ISSN | 0271-4132 |

## Cite this

Anbar Meidl, N., Beelen, P., & Nguyen, N. (2017). The Exact Limit of Some Cubic Towers. In

*Proceedings of the International Conference on Arithmetic, Geometry, Cryptography and Coding theory (2015)*American Mathematical Society. Contemporary Mathematics, Vol.. 686