… of spherical design is given in terms of harmonic polynomials. In this paper, we define a
spherical design of harmonic index t … is a spherical design of harmonic index attaining the bound. …

… lower bounds for the sizes of spherical designs of harmonic index t (or for harmonic index
T). We also study ‘tight’ spherical designs of harmonic index t or index T. Here ‘tight’ means …

… is to study spherical designs of harmonic index t as well as harmonic index T for some T, and
… are Fisher type lower bounds for spherical designs of harmonic index t and T, as well as the …

… for spherical codes introduced by Bachoc and Vallentin (2008). As a corollary to our bound,
we show the nonexistence of spherical tight designs of harmonic index 4 on a sphere in R n …

… A recent proof of a conjecture on spherical design, synonym of equal-weight cubature
formulas, by Bondarenko, Radchenko, and Viazovska, is included, for which the necessary …

… A design consideration of a permanent magnet spherical motor (PMSM) … design according
to future control effect. This paper can provide a reference for design and control of spherical …

… of spherical tight designs of harmonic index 4 on Sn−1 with n ≥ 3. … harmonic polynomial
function f on Rn of degree t. Our concern in this paper is in tight harmonic index 4-designs. A …

… consider spherical designs of harmonic index Tm, or spherical Tm-design for brevity,
where Tm is defined in (2). It is clear that any pair of antipodal points forms a spherical Tm-design …

… design theoretical viewpoint and the code theoretical viewpoint. We will discuss examples of
spherical t -designs, including tight t -designs, ie t -designs … Also, we see that tight t -designs …

… When observations are available over either the whole sphere or (as will be shown in this
paper) a hemisphere, the problem can be solved by the usual method of spherical harmonic …