Date | 2023-06-15 |
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Speaker | Olivier Carton |

Dept. | IRIF, Univ. of Paris Cite, France |

Room | 129-406 |

Time | 16:00-17:00 |

M. B. Levin constructed a real number x such that the first N terms of the sequence b^n x mod 1 for n >= 1 have discrepancy $O((log N)^2/N)$. This is the lowest discrepancy known for this kind of sequences. In this talk, we present Levin's construction in terms of nested perfect necklaces, which are a variant of the classical de Bruijn sequences. For base 2 and the order being a power of 2, we give the exact number of nested perfect necklaces and an explicit method based on matrices to construct each of them.

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