Existence of (2, 8) GWhD( v) and (4, 8) GWhD( v) with $${ v \equi v 0,1 (mod 8)}$$期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Existence of (2, 8) GWhD( v) and (4, 8) GWhD( v) with $${ v \equi v 0,1 (mod 8)}$$

Authors:	R Julian R Abel Norman J Finizio Malcolm Greig Luis B Morales

Institution:	(1) School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia;(2) Department of Mathematics, University of Rhode Island, Kingston, RI 02881, USA;(3) Greig Consulting, 317–130 Eleventh St. East, North Vancouver, BC, Canada, V7L 4R3;(4) IIMAS, Universidad Nacional, Autonoma de Mexico, Mexico, DF, 04510, Mexico

Abstract:	(2, 8) Generalized Whist tournament Designs (GWhD) on v players exist only if ${v \equiv 0,1 (mod 8)}$ . We establish that these necessary conditions are sufficient for all but a relatively small number of (possibly) exceptional cases. For ${v \equiv 1 (mod 8)}$ there are at most 12 possible exceptions: {177, 249, 305, 377, 385, 465, 473, 489, 497, 537, 553, 897}. For ${v \equiv 0 (mod 8)}$ there are at most 98 possible exceptions the largest of which is v = 3696. The materials in this paper also enable us to obtain four previously unknown (4, 8)GWhD(8n+1), namely for n = 16,60,191,192 and to reduce the list of unknown (4, 8) GWhD(8n) to 124 values of v the largest of which is v = 3696.

Keywords:	Generalized Whist tournament BIBD Resolvable Nearly resolvable Frame
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