Some recent developments on BIBDs and related designs

DOI10.1016/0012-365X(93)90016-MzbMath0795.05026OpenAlexW2013275995MaRDI QIDQ1313979

Lie Zhu

Publication date: 11 September 1994

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(93)90016-m

zbMATH Keywords

BIBDgroup divisible designsGDDcovering designsGD designspacking designs

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05)

Related Items (31)

Balanced semi-Latin rectangles: properties, existence and constructions for block size two ⋮ Group divisible packings and coverings with any minimum leave and minimum excess ⋮ Constructions of Sarvate-Beam group divisible designs ⋮ General frame constructions for \(\mathbb{Z}\)-cyclic triplewhist tournaments ⋮ On the maximum double independence number of Steiner triple systems ⋮ The spectrum of semicyclic holey group divisible designs with block size three ⋮ Orthogonal cycle systems with cycle length less than 10 ⋮ Completely reducible super-simple designs with block size four and related super-simple packings ⋮ A bound for Wilson's general theorem ⋮ Balanced incomplete block designs with block size 9. II. ⋮ HGDDs with block size four. ⋮ The existence spectrum for \((3,\lambda)\)-GDDs of type \(g^t u^1\) ⋮ Super-simple group divisible designs with block size 4 and index \(\lambda = 7,8\) ⋮ Determining the spectrum of \(\mathrm{Meta}(K_{4}+e>K_{4},\lambda)\) for any \(\lambda\) ⋮ \(w\)-cyclic holey group divisible designs and their application to three-dimensional optical orthogonal codes ⋮ Semi-cyclic holey group divisible designs with block size three ⋮ Generalizing Clatworthy group divisible designs ⋮ RHPMDs and FHPMDs with \(k=4\) and type \(4^u\) ⋮ The existence of HGDDs with block size four and its application to double frames ⋮ Semi-cyclic Holey Group Divisible Designs and Applications to Sampling Designs and Optical Orthogonal Codes ⋮ A New Construction of Group Divisible Designs with Nonuniform Group Type ⋮ Kirkman covering designs with even-sized holes ⋮ The existence of BIB designs ⋮ Two-weight codes: upper bounds and new optimal constructions ⋮ Super-simple group divisible designs with block size 4 and index 5 ⋮ On group divisible covering designs ⋮ Existence of holey 3-GDDs of type \((u,g^t w^1)\) ⋮ The existence of resolvable BIBD with \(\lambda=1\) ⋮ Two-dimensional balanced sampling plans avoiding adjacent units ⋮ A general construction for optimal cyclic packing designs ⋮ A linear hypergraph extension of Turán's theorem

Cites Work

• Resolvable group divisible designs with block size 3
• Incomplete self-orthogonal latin squares \(ISOLS(6m+6,2m)\) exist for all m
• On large sets of disjoint Steiner triple systems. VI
• On large sets of disjoint Steiner triple systems. III
• On small packing and covering designs with block size 4
• On the covering of pairs by quadruples
• Frames for Kirkman triple systems
• Coverings of pairs by quintuples
• Coverings pairs by quintuples: The case v congruent to 3 (mod 4)
• A general construction for group-divisible designs
• Subspaces of linear spaces of line size 4
• On the number of disjoint Mendelsohn triple systems
• A few more RBIBDs with \(k=5\) and \(\lambda{}=1\)
• An existence theory for pairwise balanced designs. III: Proof of the existence conjectures
• A theorem on the maximum number of disjoint Steiner triple systems
• Balanced incomplete block designs and related designs
• Group divisible designs with block-size four
• Further cases of double resolvability
• Optimal packings of \(K_4\)'s into a \(K_n\)
• Embeddings on \(S(2,4,v)\)
• Existence of resolvable BIBDs with \(k=5\) and \(\lambda=4\)
• Double resolvability of some complete 3-designs
• Kirkman packing designs KPD\((\{3, 5^*\},v)\)
• BIBD's with block-size seven
• Symmetric Mendelsohn triple system and large sets of disjoint Mendelsohn triple systems
• Finite bases for some PBD-closed sets
• Sylvester's problem of the 15 schoolgirls
• Embeddings of resolvable triple systems
• Four new BIBDs with block size seven
• On the covering of pairs by quadruples. II
• On resolvable designs
• Embeddings of Steiner triple systems
• Frames with Block Size Four
• Bounds for binary codes of length less than 25
• Embeddings of S_λ(2, 4, v)
• Two new direct product‐type constructions for resolvable group‐divisible designs
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