Sun, Hsin-Min On the existence of simple BIBDs with number of elements a prime power. (English) Zbl 1258.05009 J. Comb. Des. 21, No. 1-2, 47-59 (2013). Summary: We show that, when the number of elements is a prime power \(q\), in many situations the necessary conditions \[ \begin{aligned} \lambda(q-1) &\equiv 0 \mod (k-1), \tag{1}\\ \lambda q(q-1) &\equiv 0 \mod k(k-1), \text{ and} \tag{2}\\ z\lambda &\leq \binom{q-2}{k-2} \tag{3} \end{aligned} \]are also sufficient for the existence of a \((q,k,\lambda)\) simple balanced incomplete block design. Cited in 1 ReviewCited in 4 Documents MSC: 05B05 Combinatorial aspects of block designs Keywords:balanced incomplete block design; finite field; generating block PDFBibTeX XMLCite \textit{H.-M. Sun}, J. Comb. Des. 21, No. 1--2, 47--59 (2013; Zbl 1258.05009) Full Text: DOI References: [1] Abel, The CRC Handbook of Combinatorial Designs pp 392– (2007) [2] Beth, Design Theory (1999) [3] Colbourn, The CRC Handbook of Combinatorial Designs (2007) · Zbl 1101.05001 [4] Sun, From planar nearrings to generating blocks, Taiwanese J Math 14 (5) pp 1713– (2010) · Zbl 1228.05081 [5] Wilson, Cyclotomy and difference families in elementary abelian groups, J Number Theory 4 pp 17– (1972) · Zbl 0259.05011 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.