Abstract
In this paper, we consider the action of (2, q) on the finite projective line \({\mathbb{F}}_q\cup\{\infty\}\) for q ≡ 1 (mod 4) and construct several infinite families of simple 3-designs which admit PSL(2, q) as an automorphism group. Some of the designs are also minimal. We also indicate a general outline to obtain some other algebraic constructions of simple 3-designs.
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Cameron PJ, Maimani HR, Omidi GR and Tayfeh-Rezaie B (2006). 3-designs from PSL(2, q). Discrete Math 306(23): 3063–3073
Dickson LE (1958). Linear groups with an exposition of the Galois theory. Dover Publications Inc., New York
Denniston RHF (1976). Some new 5-designs. Bull Lond Math Soc 8: 263–267
Grannell MJ, Griggs TS and Mathon RA (1993). Some Steiner 5-designs with 108 and 132 points. J Combin Des 1: 213–238
Hughes D (1965). On t-designs and groups. Am J of Math 87: 761–778
Huppert B (1967). Endliche Gruppen I. Springer Verlag, Berlin
Mohacsy H and Ray-Chaudhuri D (2003). A construction for group divisible t-designs with strength t ≥ 2 and index unity. J Statist Plann Inference 109: 167–177
Mills WH (1978). A new 5-design. Ars Combin 6: 193–195
Li W, The existence of a simple 3 − (30, 7, 15) Design and a simple 3 − (26, 12, 55) Design. Preprint
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Balachandran, N., Ray-Chaudhuri, D. Simple 3-designs and PSL(2, q) with q ≡ 1 (mod 4). Des. Codes Cryptogr. 44, 263–274 (2007). https://doi.org/10.1007/s10623-007-9096-z
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DOI: https://doi.org/10.1007/s10623-007-9096-z