From 3257846a4daca54c53cd3d9a971e3fdbbe44ba54 Mon Sep 17 00:00:00 2001
From: "Victor V. Albert" <valbert4@gmail.com>
Date: Sat, 22 Jun 2024 14:59:07 -0400
Subject: [PATCH] ~

---
 .../properties/block/universally_optimal/t-designs.yml      | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/codes/classical/properties/block/universally_optimal/t-designs.yml b/codes/classical/properties/block/universally_optimal/t-designs.yml
index 7545a3c69..38d1844a6 100644
--- a/codes/classical/properties/block/universally_optimal/t-designs.yml
+++ b/codes/classical/properties/block/universally_optimal/t-designs.yml
@@ -20,13 +20,13 @@ description: |
   Such a design is called a combinatorial design (a.k.a. block design or covering design) \cite{manual:{Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973): vi+-97.}}.
   Designs on the full space of binary string (Hamming space) are called orthogonal arrays.
 
-  More generally, designs exist when \(X\) is \(q\)-ary Hamming space (where they are called orthogonal arrays), ordered Hamming space \cite{doi:10.4153/CJM-1999-017-5,arXiv:cs/0702033}, \(q\)-ary Johnson space (where they are called subspace designs), a sphere \cite{doi:10.1007/BF03187604} (where they are called spherical designs), or a compact connected two-point homogeneous space \cite{doi:10.1109/18.720545,preset:LevBounds,arXiv:1308.3188} (the sphere or the real, complex, quaternionic, or octonionic projective spaces \cite{doi:10.2307/1969427}).
+  More generally, designs exist when \(X\) is \(q\)-ary Hamming space (where they are called orthogonal arrays), ordered Hamming space \cite{doi:10.4153/CJM-1999-017-5,arXiv:cs/0702033}, \(q\)-Johnson space \cite{manual:{Cameron, Peter J. "Generalisation of Fisher’s inequality to fields with more than one element." Combinatorics, London Math. Soc. Lecture Note Ser 13 (1973): 9-13.},doi:10.1145/2488608.2488715} (where they are called subspace designs), a sphere \cite{doi:10.1007/BF03187604} (where they are called spherical designs), or a compact connected two-point homogeneous space \cite{doi:10.1109/18.720545,preset:LevBounds,arXiv:1308.3188} (the sphere or the real, complex, quaternionic, or octonionic projective spaces \cite{doi:10.2307/1969427}).
   Complex projective designs are designs on the space of all quantum states \cite{arXiv:quant-ph/0310075,arxiv:quant-ph/0701126,doi:10.1017/9781139207010}.
 
   Designs can also exist on groups.
   Designs on the unitary (projective unitary) group are called strong unitary (unitary) designs \cite{arXiv:quant-ph/0611002}, while \(t\)-designs on the permutation group are called permutation \(t\)-designs \cite{doi:10.1017/S0963548300001917} (a.k.a. \(t\)-wise independent permutations).
 
-  Other notable designs include torus designs \cite{arXiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1}, and (exact) quadrature/cubature formulas for integration over the reals \cite{doi:10.1017/S0962492900002701,doi:10.1137/1015023,doi:10.1016/S0885-064X(03)00011-6,doi:10.18434/M3167}.
+  Other notable designs include torus designs \cite{arXiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939}, and (exact) quadrature/cubature formulas for integration over the reals \cite{doi:10.1017/S0962492900002701,doi:10.1137/1015023,doi:10.1016/S0885-064X(03)00011-6,doi:10.18434/M3167}.
   Existence has been proven for combinatorial designs \cite{doi:10.1016/0012-365X(87)90061-6}, subspace designs \cite{doi:10.1016/j.jcta.2014.06.001,arxiv:2212.00870}, as well as designs on continuous topological spaces \cite{doi:10.1016/0001-8708(84)90022-7}.
 
 #  when restricted to act on distinct \(t\)-tuples; see \cite[Remarks 6-7]{arXiv:2404.14648}
@@ -42,3 +42,5 @@ _meta:
   changelog:
     - user_id: VictorVAlbert
       date: '2024-06-19'
+    - user_id: AlexanderBarg
+      date: '2024-06-19'