zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The packing problem in statistics, coding theory and finite projective spaces: Update 2001. (English) Zbl 1025.51012
Blokhuis, A. (ed.) et al., Finite geometries. Proceedings of the fourth Isle of Thorns conference, Brighton, UK, April 2000. Dordrecht: Kluwer Academic Publishers. Dev. Math. 3, 201-246 (2001).

The packing problem in statistics, coding theory and finite projective spaces regards the determination of the maximal or minimal sizes of given subconfigurations of finite projective spaces. The problem is not only interesting from a geometrical point of view; it also arises when coding theoretical problems and problems from the design of experiments are translated into equivalent geometrical problems. The geometrical interest in the packing problem and the links with problems investigated in other research fields have given this problem a central place in Galois geometries, that is, the study of finite projective spaces.

The paper under review is an excellent survey of recent results concerning the packing problem. That paper updates the authors’ 1998 survey on the same theme that was written for Bose Memorial Conference (Colorado, June 7-11, 1995) [J. Stat. Plann. Inference 72, No. 1-2, 355-380 (1998; Zbl 0958.51013)]. Since then, considerable progress has been made on the following kinds of subconfigurations: n-arcs in PG(2,q), n-arcs in PG(N,q), n-caps in PG(N,q), (n,r)-arcs in PG(2,q), multiple blocking sets in PG(2,q), blocking sets in PG(N,q), n-tracks and almost MDS codes, minihypers.

Many open questions are presented in the paper, and a comprehensive bibliography of 229 references is compiled.

MSC:
51E23Spreads and packing problems (geometry)
94B05General theory of linear codes
51E22Linear codes and caps in Galois spaces