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Ling, Alan C. H.; Zhu, Xiaojun; Colbourn, Charles J.; Mullin, R. C.

doi:10.1023/a:1008248521550

Cited by 31 publications

(4 citation statements)

References 6 publications

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“…Theorem 1.5 (Arc construction) [13]. If q is a prime power, n is a positive integer such that 1 n q&1, and t is a positive integer such that 0 t q+1&n, then nq+t # B([n, n+1, n+2, q]).…”

Section: Introductionmentioning

confidence: 99%

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Pairwise Balanced Designs with Block Sizes 8, 9, and 10

Colbourn

Ling

1997

Journal of Combinatorial Theory, Series A

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“…Theorem 1.5 (Arc construction) [13]. If q is a prime power, n is a positive integer such that 1 n q&1, and t is a positive integer such that 0 t q+1&n, then nq+t # B([n, n+1, n+2, q]).…”

Section: Introductionmentioning

confidence: 99%

“…Lemma 1.7 [13]. If q is an odd prime power, then for any integer t such that 0 t q+1, we have q(q&1)Â2+t…”

Section: Introductionmentioning

confidence: 99%

Pairwise Balanced Designs with Block Sizes 8, 9, and 10

Colbourn

Ling

1997

Journal of Combinatorial Theory, Series A

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“…We now provide updated lists of the unknown elements of BðKÞ in [11], [22], and [12] for all subsets K of f5; 6; 7; 8; 9g containing 5 except K ¼ f5; 7g and f5; 8g; see Theorems 8.2 and 9.2 for these. Known definite exceptions in these lists are given in bold.…”

mentioning

confidence: 99%

“…Known definite exceptions in these lists are given in bold. For K ¼ f5; 6g, f5; 6; 7g; and f5; 6; 7; 8g, there are no improvements here to the tables in [11], [12], or [22], while K ¼ f5; 6; 7; 8; 9g is completely solved in [22].…”

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confidence: 99%

Quintessential PBDs and PBDs with prime power block sizes ≥ 8

Abel

Bennett

2004

J of Combinatorial Designs

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In this paper, we look at the existence of ðv v; KÞ pairwise balanced designs (PBDs) for a few sets K of prime powers ! 8 and also for a number of subsets K of f5; 6; 7; 8; 9g, which contain f5g. For K ¼ f5; 7g; f5; 8g; f5; 7; 9g, we reduce the largest v v for which a ðv v; KÞ-PBD is unknown to 639, 812, and 179, respectively. When K is Q !8 , the set of all prime powers ! 8, we find several new designs for 1,180 v v 1,270, and reduce the largest unsolved case to 1,802. For K ¼ Q 0;1;5ð8Þ , the set of prime powers ! 8 and 0; 1, or 5 (mod 8) we reduce the largest unknown case from 8,108 to 2,612. We also obtain slight improvements when K is one of f8; 9g or Q 0;1ð8Þ , the set of prime powers 0 or 1 (mod 8).

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On c‐Bhaskar Rao designs with block size 4

Greig¹,

Hurd

McCranie³

et al. 2002

J of Combinatorial Designs

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Several new families of c-Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c-BRDðv v; 4; kÞ are that:It is proved that these conditions are necessary, and are sufficient for most pairs of c and k; in particular, they are sufficient whenever k À c 6 ¼ 2 for c ! 0 and whenever c À k min 6 ¼ 2 for c < 0. For c > 0, the necessary conditions are sufficient for v v > 101; for the classic Bhaskar Rao designs, i.e., c ¼ 0, we show the necessary conditions are sufficient with the possible exception of 0-BRDðv v; 4; 2Þ's for v v 4 ðmod 6Þ.

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Cited by 31 publications

References 6 publications

Pairwise Balanced Designs with Block Sizes 8, 9, and 10

Pairwise Balanced Designs with Block Sizes 8, 9, and 10

Quintessential PBDs and PBDs with prime power block sizes ≥ 8

On c‐Bhaskar Rao designs with block size 4

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