Super‐simple resolvable balanced incomplete block designs with block size 4 and index 2

Abstract

Abstract:The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient.

Ordered tournaments and ordered triplewhist tournaments with the three person property

“…9 (2,36,23,14), (3,27,21,14), (3,22,1,29), (2, 43, 14, 1), (2,3,6,29), (4,22,18,6), (4,43,12,26), (1,9,37,8), (3,6,14,12). 11 (3,39,36,37), (2,26,18,14), (3,26,4,17), (4,43,17,46), (1,7,8,54), (2,46,53,…”

“…45 (1,3,5,21), (4,43,6,34), (33,41,14,29), (7,25,32,10), (44,12,31,28), (13,17,8,18), (22,2,15,39), (40,9,19,26), (38,37,16,27), (35,30,24,36), (20,11,23,42). 49 (42, 40, 39, 24), (27,48,44,3), (23,45,10,16), (46,37,28,…”

“…11 (3,39,36,37), (2,26,18,14), (3,26,4,17), (4,43,17,46), (1,7,8,54), (2,46,53,19), (4,42,48,36), (3,36,17,19), (2,9,36,33), (2,43,34,6), (1,38,27,19). (0, 19, 2, 1), (6,37,9,33), (16,18,22,19), (29,2,13,…”

“…For n = 7, the required design is over ( g Initial Games 8 (4, 21, 27, 13), (2,26,23,14), (1,7,3,14), (1,37,4,3), (2,29,28,16), (3,22,39,21), (1,8,19,17), (2, 39, 31, 23). 9 (2,36,23,14), (3,27,21,14), (3,22,1,29), (2, 43, 14, 1), (2,3,6,29), (4,22,18,6), (4,43,12,26), (1,9,37,8), (3,…”

Existence of Z-cyclic 3PDTWh(p) for Prime p ≡ 1 (mod 4)

“…This kind of design was introduced and studied by Gronau and Mullin [29] and also studied by Chen [15,16]. Such designs with resolvable property were investigated by Ge and Lam [25] and Zhang and Ge [38].…”