Abstract
An extending theorem for s-resolvable t-designs is presented, which may be viewed as an extension of Qiu-rong Wu’s result. The theorem yields recursive constructions for s-resolvable t-designs, and mutually disjoint t-designs. For example, it can be shown that if there exists a large set LS[29](4, 5, 33), then there exists a family of 3-resolvable 4-\((5+29m, 6, \frac{5}{2}m(1+29m) )\) designs for \(m \ge 1,\) with 5 resolution classes. Moreover, for any given integer \(h \ge 1\), there exist \((5\cdot 2^h-5)\) mutually disjoint simple 3-\((3+m(5\cdot 2^h-3),4,m)\) designs for all \(m \ge 1.\) In addition, we give a brief account of t-designs derived from the result of Wu.
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Communicated by L. Teirlinck.
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van Trung, T. An extending theorem for s-resolvable t-designs. Des. Codes Cryptogr. 89, 589–597 (2021). https://doi.org/10.1007/s10623-020-00835-7
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DOI: https://doi.org/10.1007/s10623-020-00835-7