Super-regular Steiner 2-designs

Buratti, Marco; Nakić, Anamari

doi:10.1016/j.ffa.2022.102116

Cited by 9 publications

(3 citation statements)

References 27 publications

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“…Uniform strong difference families have been implicitly used in the literature for many years and they have been formally introduced for the first time in [4]. Since then, they have been explicitly used in many papers [3,9,10,11,14,16,17,20,23,28]. Non-uniform SDFs have been used in [6] for the construction of the so-called Hadamard partitioned difference families also considered in [24].…”

Section: Harmonious Strong Difference Familiesmentioning

confidence: 99%

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Partitioned difference families: The storm has not yet passed

Buratti¹,

Jungnickel²

2023

AMC

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Two years ago, we alarmed the scientific community about the large number of bad papers in the literature on zero difference balanced functions, where direct proofs of seemingly new results are presented in an unnecessarily lengthy and convoluted way. Indeed, these results had been proved long before and very easily in terms of difference families.In spite of our report, papers of the same kind continue to proliferate. Regrettably, a further attempt to put the topic in order seems unavoidable. While some authors now follow our recommendation of using the terminology of partitioned difference families, their methods are still the same and their results are often trivial or even wrong. In this note, we show how a very recent paper of this type can be easily dealt with.

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Section: Harmonious Strong Difference Familiesmentioning

confidence: 99%

“…Indeed it is readily seen that we have P i + 1 = P i+1 (mod 4) , hence the group Z 8 of translations modulo 8 acts sharply transitively on Z 8 and transitively on R. If in the above example we add an extra point, say ∞, to the blocks of size 2 we get an AHS (2,3,9).…”

Section: Introductionmentioning

confidence: 99%

Partitioned difference families: The storm has not yet passed

Buratti¹,

Jungnickel²

2023

AMC

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“…The number of pairwise non-isomorphic 2 − (81, 6, 2) designs is at least equal to 2. Some infinite classes of strictly additive 2-designs will be given in a future paper still in preparation [2].…”

Section: Introductionmentioning

confidence: 99%

The first example of a simple 2−(81,6,2) design

Nakić

2021

Examples and Counterexamples

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Extensions of Steiner Triple Systems

Falcone,

Figula,

Galici

2025

J of Combinatorial Designs

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In this article, we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a powerful method for constructing Steiner triple systems containing Veblen points.

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Super-regular Steiner 2-designs

Cited by 9 publications

References 27 publications

Partitioned difference families: The storm has not yet passed

Partitioned difference families: The storm has not yet passed

The first example of a simple 2−(81,6,2) design

Extensions of Steiner Triple Systems

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