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arXiv · 2505.05894

Comment and correction for "On Explicit Construction of Simplex $t$-designs" by M. S. Baladram

Jakub Czartowski
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Abstract

In [Bal18] a new method of constructing simplex designs based on cyclic group on $n$ elements has been proposed. One of the claims put forward therein is existence of 3-point simplex 3-design in dimension $d = 3$. In this manuscript we present explicit counterarguments and suggest a manner to rectify the existing proofs. By doing this, we show that the results presented in [Bal18] can be utilised to construct simplex 3-designs scaling as $d^2$, which suggest a general scaling of $d^{t-1}$. Finally, we put forward a notion that encompasses the objects conforming with bounds given in [Bal18], which we refer to as symmetry-restricted simplex $t$-designs.

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Jakub Czartowski. 2025-05-09. Comment and correction for "On Explicit Construction of Simplex $t$-designs" by M. S. Baladram. https://arxiv.org/abs/2505.05894

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