caa a22 4500 445830662 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10255-011-0080-z doi (NATIONALLICENCE)springer-10.1007/s10255-011-0080-z Incomplete group divisible designs with block size four and general index [Elektronische Daten] [Li-dong Wang, Hai-rong Kong, Hong-juan Liu] In this paper, we investigate the existence of incomplete group divisible designs (IGDDs) with block size four, group-type (g, h) u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg(u − 1) ≡ 0 (mod 3), λ(g − h)(u−1) ≡ 0 (mod 3), and ⇌u(u − 1)(g 2 − h 2) ≡ 0 (mod 12). These necessary conditions are shown to be sufficient for all λ ≥ 2. The known existence result for λ = 1 is also improved. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 group divisible design nationallicence incomplete group divisible design nationallicence holy group divisible design nationallicence Wang Li-dong Department of Basic Courses, Chinese People's Armed Police Force Academy, 065000, Langfang, China aut Kong Hai-rong School of Science, Hebei University of Technology, 300401, Tianjin, China aut Liu Hong-juan Department of Computer Science and Engineering, Langfang Polytechnic Institute, 065000, Langfang, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 407-418 0168-9673 27:3<407 2011 27 10255 https://doi.org/10.1007/s10255-011-0080-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0080-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Li-dong Department of Basic Courses, Chinese People's Armed Police Force Academy, 065000, Langfang, China aut NATIONALLICENCE 700 1- Kong Hai-rong School of Science, Hebei University of Technology, 300401, Tianjin, China aut NATIONALLICENCE 700 1- Liu Hong-juan Department of Computer Science and Engineering, Langfang Polytechnic Institute, 065000, Langfang, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 407-418 0168-9673 27:3<407 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer