## Abstract

The (N, t, m) lottery problem seeks the smallest possible set of tickets (t-subset of {1, 2,..., N}) that guarantees at least one ticket with m correct matches, for any t-subset drawn randomly by the house. The design of a minimal set of tickets with such property is an open problem for most (N,t, m) values.

Here, we modify the problem. We seek a set of tickets that guarantees several tickets having m correct matches for any draw of the house, and use a Monte Carlo algorithm for constructing such sets.

For the (49, 6, 3) lottery this algorithm constructs a family of 1293 tickets where, for any drawn 6-tuple, at least 20 tickets win 3 matches. The ratio 1293/20 is smaller than the number tickets of the best known (49, 6, 3) lottery design (174), and also smaller than the theoretical lower bound on the size of such design (87).

Here, we modify the problem. We seek a set of tickets that guarantees several tickets having m correct matches for any draw of the house, and use a Monte Carlo algorithm for constructing such sets.

For the (49, 6, 3) lottery this algorithm constructs a family of 1293 tickets where, for any drawn 6-tuple, at least 20 tickets win 3 matches. The ratio 1293/20 is smaller than the number tickets of the best known (49, 6, 3) lottery design (174), and also smaller than the theoretical lower bound on the size of such design (87).

Original language | English |
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Pages (from-to) | 73-80 |

Number of pages | 8 |

Journal | Monte Carlo Methods and Applications |

Volume | 7 |

Issue number | 1-2 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics