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Abel, R. Julian R.; Combe, Diana; Nelson, Adrian M.; Palmer, William D.

Block designs signed over groups of order \(2^n 3^m\). (English) Zbl 1370.05021

Discrete Math. 340, No. 12, 2925-2940 (2017).
Summary: We introduce a new piecewise construction technique for generalised Bhaskar Rao designs and the concepts of generalised Bhaskar Rao block design pieces and holey generalised Bhaskar Rao block designs. We prove composition theorems for these designs. Using this construction technique and the theory of group representations, and the representations of 2-groups over the field with 3 elements, we show that the established necessary conditions for the existence of generalised Bhaskar Rao designs of block size 3 are sufficient for all groups of order \(2^n 3^m\).

Cited in 1 Document

MSC:

05B05 Combinatorial aspects of block designs
05B30 Other designs, configurations

Keywords:

\(\mathbb{G}\)-signed block design; design piece; holey design; generalised Bhaskar Rao block design; generalised Bhaskar Rao design; group divisible design

Software:

GAP
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Full Text: DOI

References:

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