Existence of (2,8) GWhD(v) and (4,8) GWhD(v) with v equivalent to 0, 1 (mod 8)
(2, 8) Generalized Whist tournament Designs (GWhD) on v players exist only if v = 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 = 1 (mod 8) there are at most 12 possible exceptions: {177, 249, 305, 377, 385, 465, 473, 489, 497, 537, 553, 897}. For v = 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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