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On the Existence of Large Sets of t-designs of Prime Sizes

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Abstract

In this paper, we employ the known recursive construction methods to obtain some new existence results for large sets of t-designs of prime sizes. We also present a new recursive construction which leads to more comprehensive theorems on large sets of sizes two and three. As an application, we show that for infinitely many values of block size, the trivial necessary conditions for the existence of large sets of 2-designs of size three are sufficient.

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Authors and Affiliations

  1. Institute for studies in theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran

    B. Tayfeh-Rezaie

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  1. B. Tayfeh-Rezaie
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Correspondence to B. Tayfeh-Rezaie.

Additional information

AMS Classification: 05B05

Communicated by:L. Teirlinck

This research was in part supported by a grant from IPM (No. 83050312).

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Tayfeh-Rezaie, B. On the Existence of Large Sets of t-designs of Prime Sizes. Des Codes Crypt 37, 143–149 (2005). https://doi.org/10.1007/s10623-004-3809-3

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  • DOI: https://doi.org/10.1007/s10623-004-3809-3

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