Efficient Spherical Designs
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Efficient Spherical Designs with Good Geometric Properties

Rob Womersley
School of Mathematics and Statistics
UNSW Sydney

Last updated 4-Feb-2017

Spherical t-designs on S2 with N = t2/2 + t + O(1) points

  • File for points sets for degrees t = 1, 2, 3, ..., 179, 180:   SF29-Nov-2012.zip (28.7 MB)
  • See here for individual point sets and more information on spherical design criteria and their geometric properties.

Symmetric (antipodal) spherical t-designs on S2 with N = t2/2 + t/2 + O(1) points

  • File of points sets for degrees t = 1, 3, 5, ..., 325:   SS31-Mar-2016.zip (82.5 MB)
  • See here for individual point sets and more information on symmetric spherical designs and their geometric properties.
  • Recent updates (available from individual point sets page below and included in .zip file)
    • Added t = 287 on 19 May 2015
    • Added t = 289 on 23 May 2015
    • Added t = 297 on 4 June 2015
    • Added t = 279, 295, 301 on 15 June 2015. Point sets for t = 279, 295 currently have somewhat high mesh ratios.
    • Added t = 293 on 19 June 2015
    • Updated t = 279 with better mesh ratio on 24 June 2015
    • Added t = 291, 299 on 24 September 2015
    • Updated t = 89, 111, 117, 203, 213, 241, 279, 295, with better mesh ratios on 24 September 2015
    • Updated t = 111, 259, 279, 295 with better mesh ratios on 21 October 2015
    • Updated t = 299 with better mesh ratio on 28 October 2015
    • Updated t = 251, 281 with better mesh ratio on 29 November 2015
    • Added t = 303, 305, 309, 311 on 29 November 2015
    • Updated t = 299 with better mesh ratio on 26 January 2016
    • Added t = 313, 315, 317, 321 on 26 January 2016
    • Updated t = 315 with better mesh ratio on 18 February 2016
    • Added t = 319, 323 on 18 February 2016
    • Updated t = 299 with better mesh ratio on 27 March 2016
    • Added t = 325 on 31 March 2016
    • Point sets for t = 323, 325 have slightly high mesh ratios.

Spherical t-designs on S3 with N = t3/9 + O(t2) points

  • S3SD     Last updated 22-Aug-2017.

Reference

  • EffSphDes.pdf to appear in Festschrift for the 80th Birthday of Ian H. Sloan, Editors Josef Dick, Frances Y Kuo and Henryk Wozniakowski (2018).

Reported at

Acknowledgement

This research includes extensive computations using the Linux computational cluster Katana supported by the Faculty of Science, UNSW Sydney.