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.
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Abel, R.J.R., Finizio, N.J., Greig, M. et al. Existence of (2, 8) GWhD(v) and (4, 8) GWhD(v) with \({v \equiv 0,1 (mod 8)}\) . Des. Codes Cryptogr. 51, 79–97 (2009). https://doi.org/10.1007/s10623-008-9245-z
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DOI: https://doi.org/10.1007/s10623-008-9245-z