The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
Abstract
We addressthe question: How should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The resuIts of extensive computations for modest values of N, n, m are described, as well as a reformulation of the problem that was suggested by these computations. The reformulation gives a way to describe n-dimensional subspaces of m-space as points on a sphere in dimension ½(m–l)(m+2), which provides a (usually) lowerdimensional representation than the Plücker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multidimensional data via Asimov's grand tour method.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Principles of Algebraic Geometry
Griffiths, P., & Harris, J. (1994) · Wiley · doi:10.1002/9781118032527 · Cited by 6,765
Sphere Packings, Lattices and Groups
Conway, J. H., & Sloane, N. J. A. (1993) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-1-4757-2249-9 · Cited by 880
Self-citation
Cited by
A sparse signal reconstruction perspective for source localization with sensor arrays
Malioutov, D., Cetin, M., & Willsky, A. S. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.850882 · Cited by 2,638
Quantum error correction via codes over GF(4)
Calderbank, A. R., Rains, E. M., Shor, P. M., & Sloane, N. J. A. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.681315 · Cited by 1,742
Self-citationGrassmannian beamforming for multiple-input multiple-output wireless systems
Love, D. J., Heath, R. W., & Strohmer, T. (2003) · IEEE Transactions on Information Theory · doi:10.1109/tit.2003.817466 · Cited by 1,505
Grassmannian frames with applications to coding and communication
Strohmer, T., & Heath, R. W. (2003) · Applied and Computational Harmonic Analysis · doi:10.1016/s1063-5203(03)00023-x · Cited by 955
On beamforming with finite rate feedback in multiple-antenna systems
Kiran Mukkavilli, K., Sabharwal, A., Erkip, E., & Aazhang, B. (2003) · IEEE Transactions on Information Theory · doi:10.1109/tit.2003.817433 · Cited by 906
Metadata
- Authors
- Conway, J. H., Hardin, R. H., & Sloane, N. J. A.
- Venue
- Experimental Mathematics
- Publisher
- Informa UK Limited
- Published
- 1996-01
- Volume
- 5
- Issue
- 2
- Pages
- 139-159
- ISSN
- 1058-6458 (ISSN-L)
- 1944-950X
- OpenAlex
- W2035469609
- Cited by
- 755
- References
- 3
- FWCI
- 3.84
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Packing Lines, Planes, etc.: Packings in Grassmannian Spaces. https://app.cochat.ai/papers/10.1080/10586458.1996.10504585
- The paper
- Conway, J. H., Hardin, R. H., & Sloane, N. J. A. (1996). Packing Lines, Planes, etc.: Packings in Grassmannian Spaces. Experimental Mathematics. https://doi.org/10.1080/10586458.1996.10504585
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
