New Spherical 4-designs

Hardin, R.H. and N.J.A. Sloane, New spherical 4-designs, Discrete Mathematics 106/107 (1992) 255-264. This paper gives a number of new spherical 4-designs, and presents numerical evidence that spherical 4-designs containing n points in k-dimensional space with k G 8 exist precisely for the following values of n and k: n even and 22 for k = 1; n 2 5 for k = 2; n = 12, 14, >I6 for k=3;n~2Ofork=4;n>29fork=5;n=27,36, ~39fork=6;n~53fork=7;andn~69 for k = 8.

[1]  W. J. Studden,et al.  Optimal Experimental Designs , 1966 .

[2]  L. Haines.  The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models , 1987 .

[3]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[4]  J. Seidel,et al.  Spherical codes and designs , 1977 .

[5]  A. Neumaier.  Interval methods for systems of equations: Preface , 1991 .

[6]  R. H. Hardin,et al.  A new approach to the construction of optimal designs , 1993 .

[7]  J. H. Lint.  A survey of perfect codes , 1975 .

[8]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[9]  B. Bajnok.  Construction of spherical t-designs , 1992 .

[10]  E. Hansen,et al.  Bounding solutions of systems of equations using interval analysis , 1981 .

[11]  Z. Galil,et al.  $D$-Optimum Weighing Designs , 1980 .

[12]  Béla Bajnok.  Construction of Designs on the 2-Sphere , 1991, Eur. J. Comb..

[13]  A. Neumaier.  Interval methods for systems of equations , 1990 .

[14]  Arnold Neumaier,et al.  An improved interval Newton operator , 1986 .

[15]  R. C. St. John,et al.  D-Optimality for Regression Designs: A Review , 1975 .

[16]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[17]  R. C. St.  D-Optimality for Regression Designs: A Review , 1975 .

[18]  P. Seymour,et al.  Averaging sets: A generalization of mean values and spherical designs , 1984 .