A spherical 
-design
is a finite set 
on a sphere 
whose equal-weight average agrees with the uniform average
on 
for every polynomial 
of degree at most 
. Thus
 |
Spherical 
-designs
give the placement of 
points on a sphere for use in numerical integration with equal weights.
Delchev and Yordanov (2026) constructed explicit equal-weight spherical 5-designs on 
with at most 
points for every odd integer 
. For odd 
, an equal-weight complex
projective design of strength 3 with 
points in complex projective
space of dimension 
yields a spherical 7-design with exactly 
points.
-Designs." Ch. 44 in 
-
and 
-Designs
with Balanced Halves." 8 Oct 2026.