This paper addresses the question: how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computationsâ€¦ (More)

Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N points exist for N = 24, 26, â‰¥ 28; 7-designs for N = 24, 30, 32, 34, â‰¥ 36; 8-designs for N = 36, 40, 42, â‰¥ 44;â€¦ (More)

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 thatâ€¦ (More)

What is the tightest packing of N equal nonoverlapping spheres, in the sense of having minimal energy, i.e., smallest second moment about the centroid? The putatively optimal arrangements areâ€¦ (More)

By combining a modified version of Hooke and Jeevesâ€™ pattern search with exact or Monte Carlo moment calculations, it is possible to find I-, Dand A-optimal (or nearly optimal) designs for a wideâ€¦ (More)

Studies were carried out on SPF F344 male rats to evaluate the effects of aging and life-prolonging food restriction, without malnutrition, on rat skeleton and circulating PTH. Six-week-old F344 ratsâ€¦ (More)

Computer-generated designs in the sphere are described which have the minimal (or larger) number of runs for a full quadratic response-surface design. In the case of 3 factors, the designs have 10â€¦ (More)