Generalized whist tournament designs

Abel, R. Julian R.; Finizio, Norman J.; Greig, Malcolm; Lewis, Scott J.

doi:10.1016/s0012-365x(02)00743-4

Cited by 9 publications

(27 citation statements)

References 9 publications

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“…For generalized whist tournament designs, we have the following results (for more information see, for example, [6]). Generalized whist tournament designs provide a method of constructing splitting balanced incomplete block designs.…”

Section: Lemma 1 ([13])mentioning

confidence: 99%

Splitting balanced incomplete block designs with block size 3 × 2

Du¹

2004

J of Combinatorial Designs

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Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., ðv v; 3k; Þ-splitting BIBDs; we give the spectrum of ðv v; 3 Â 2; Þ-splitting BIBDs. As an application, we obtain an infinite class of 2-splitting A-codes. #

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Section: Lemma 1 ([13])mentioning

confidence: 99%

Splitting balanced incomplete block designs with block size 3 × 2

Du¹

2004

J of Combinatorial Designs

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“…The existence results for (4,8) GWhD(8n + 1) established in [5] make use of many well known theorems and facts together with directly constructed designs for v = 8, 16, 57, 65, Table 1 Values of n for which (t, 8) GWhD(8n + 1), t = 2, 4 were unknown 4 1 6 2 0 2 2 2 3 3 1 3 3 3 7 3 8 4 0 47 48 58 59 60 61 62 67 68 69 93 112 191 192 213 218 220 224 Table 2 Values of n for which (t, 8) GWhD(8n), t = 2, 4 were unknown …”

Section: Unsettled Casesmentioning

confidence: 99%

“…These designs were obtained from the following lemma, the proof of which gives a construction based on the log table for GF(2 n ). The construction is described in [6] and proved more deeply in [4]; see also [18]. Three examples of this lemma are given below.…”

Section: Moore Nested and 2-dimensional Gwhdsmentioning

confidence: 99%

“…If v ≡ 1 (mod k), then m = v and A = ∅. A (2, 4) GWhD(v) is the standard whist tournament (see e.g., [8]), and a (4,8) GWhD(v) is called a pitch tournament in [4][5][6]13,14]. Abel et al [4] contains many constructions for GWhDs, which we will cite as needed.…”

Section: Introductionmentioning

confidence: 99%

“…Several of the new (2,8) GWhD(v) designs presented here have the feature that a (4, 8) GWhD(v) design is obtainable from them. As a consequence we are able to make some improvements to the existence results in [5,6] for (4,8) GWhD(v) designs. In order that one can discern the presence of (4, 8) GWhD(v) designs in some of our (2,8) GWhD(v) designs we introduce several types of nested designs in Sect.…”

Section: Introductionmentioning

confidence: 99%

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

Abel

Finizio

Greig³

et al. 2008

Des. Codes Cryptogr.

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Existence of (2, 8) GWhD(v) and (4, 8) GWhD(v)with v ≡ 0, 1 (mod 8) Abstract (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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Pitch tournament designs and other BIBDs—existence results for the case ν = 8n

Abel

Finizio

Greig³

et al. 2001

J of Combinatorial Designs

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A pitch tournament is a resolvable or near resolvablevY 8Y 7 BIBD that satis®es certain criteria in addition to theusual condition that v 0 or 1 mod 8. Here we establish that for the case v 8n the necessary condition forpitch tournaments is suf®cient for all n b 1615, with at most 187 smaller exceptions. This complements our earlier study of the v 8n 1 case, where we established suf®ciency for all n b 224, with at most 28 smaller exceptions. The four missing cases for vY 8Y 7 BIBDs are provided, namely v Pf48Y 56Y 96Y 448g, thereby establishing that the necessary existence conditions are suf®cient without exception. Some constructions for resolvable designs are also provided, reducing the existence question for vY 8Y 7 RBIBDs to 21 possible exceptions.

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Generalized whist tournament designs

Cited by 9 publications

References 9 publications

Splitting balanced incomplete block designs with block size 3 × 2

Splitting balanced incomplete block designs with block size 3 × 2

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

Pitch tournament designs and other BIBDs—existence results for the case ν = 8n

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