A recursive construction for simple t-designs using resolution

2016/12/06 by Tran van Trung, van Trung, Tran
Computer Science · Decision Sciences · Engineering · #05B05 #Combinatorics (math.CO) #FOS: Mathematics #Optimal Experimental Design Methods #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1612.01978

openalex publication_date 2016/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work presents a recursive construction for simple t-designs using resolutions of the ingredient designs. The result extends a construction of t-designs in our recent paper [39]. Essentially, the method in [39] describes the blocks of a constructed design as a collection of block unions from a number of appropriate pairs of disjoint ingredient designs. Now, if some pairs of these ingredient t-designs have both a suitable s-resolution, then we can define a distance mapping on their resolution classes. Using this mapping enables us to have more possibilities for forming blocks from those pairs. The method makes it possible for constructing many new simple t-designs. We give some application results of the new construction.

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