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<h3>References</h3>


<p><a id="biBabramowitz_handbook_1972" name="biBabramowitz_handbook_1972"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>AS72</span>]    (<span class='BibEditor'>Abramowitz, M. and Stegun, I. A.</span>, Eds.),
 <i class='BibTitle'>Handbook of Mathematical Functions</i>,
 <span class='BibPublisher'>Dover</span>,
 <span class='BibAddress'>New York</span>
 (<span class='BibYear'>1972</span>).
</p>


<p><a id="biBbaez_octonions_2002" name="biBbaez_octonions_2002"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Bae02</span>]   <b class='BibAuthor'>Baez, J.</b>,
 <i class='BibTitle'>The octonions</i>,
 <span class='BibJournal'>Bulletin of the American Mathematical Society</span>,
 <em class='BibVolume'>39</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2002</span>),
 <span class='BibPages'>145--205</span>.
</p>


<p><a id="biBbannai_algebraic_2021" name="biBbannai_algebraic_2021"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BBIT21</span>]   <b class='BibAuthor'>Bannai, E., Bannai, E., Ito, T. and Tanaka, R.</b>,
 <i class='BibTitle'>Algebraic Combinatorics</i>,
 <span class='BibPublisher'>Walter de Gruyter GmbH</span>,
 <span class='BibSeries'>De {Gruyter}, {Series} in {Discrete} {Mathematics} and
      {Applications}</span> (<span class='BibNumber'>5</span>),
 <span class='BibAddress'>Berlin/Boston</span>
 (<span class='BibYear'>2021</span>)<br />
(<span class='BibNote'>OCLC: on1243061900</span>).
</p>


<p><a id="biBconway_quaternions_2003" name="biBconway_quaternions_2003"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CS03</span>]   <b class='BibAuthor'>Conway, J. H. and Smith, D. A.</b>,
 <i class='BibTitle'>On Quaternions and Octonions: Their
      Geometry, Arithmetic, and Symmetry</i>,
 <span class='BibPublisher'>CRC Press</span>
 (<span class='BibYear'>2003</span>).
</p>


<p><a id="biBconway_sphere_2013" name="biBconway_sphere_2013"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CS13</span>]   <b class='BibAuthor'>Conway, J. H. and Sloane, N. J. A.</b>,
 <i class='BibTitle'>Sphere packings, lattices and groups</i>,
 <span class='BibPublisher'>Springer Science \& Business Media</span>,
 <em class='BibVolume'>290</em>
 (<span class='BibYear'>2013</span>).
</p>


<p><a id="biBcameron_designs_1991" name="biBcameron_designs_1991"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CVL91</span>]   <b class='BibAuthor'>Cameron, P. J. and Van Lint, J. H.</b>,
 <i class='BibTitle'>Designs, graphs, codes and their links</i>,
 <span class='BibPublisher'>Cambridge University Press</span>,
 <em class='BibVolume'>3</em>,
 <span class='BibAddress'>Cambridge</span>
 (<span class='BibYear'>1991</span>).
</p>


<p><a id="biBdelsarte_spherical_1977" name="biBdelsarte_spherical_1977"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DGS77</span>]   <b class='BibAuthor'>Delsarte, P., Goethals, J. M. and Seidel, J. J.</b>,
 <i class='BibTitle'>Spherical codes and designs</i>,
 <span class='BibJournal'>Geometriae Dedicata</span>,
 <em class='BibVolume'>6</em>
 (<span class='BibYear'>1977</span>),
 <span class='BibPages'>363--388</span>.
</p>


<p><a id="biBelkies_exceptional_1996" name="biBelkies_exceptional_1996"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>EG96</span>]   <b class='BibAuthor'>Elkies, N. D. and Gross, B. H.</b>,
 <i class='BibTitle'>The exceptional cone and the Leech lattice</i>,
 <span class='BibJournal'>International Mathematics Research Notices</span>,
 <em class='BibVolume'>1996</em> (<span class='BibNumber'>14</span>)
 (<span class='BibYear'>1996</span>),
 <span class='BibPages'>665--698</span><br />
(<span class='BibNote'>Publisher: Citeseer</span>).
</p>


<p><a id="biBelkies_cubic_2001" name="biBelkies_cubic_2001"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>EG01</span>]   <b class='BibAuthor'>Elkies, N. D. and Gross, B. H.</b>,
 <i class='BibTitle'>Cubic Rings and the Exceptional Jordan
      Algebra</i>,
 <span class='BibJournal'>Duke Mathematical Journal</span>,
 <em class='BibVolume'>109</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2001</span>),
 <span class='BibPages'>383--410</span>.
</p>


<p><a id="biBfaraut_analysis_1994" name="biBfaraut_analysis_1994"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>FK94</span>]   <b class='BibAuthor'>Faraut, J. and Koranyi, A.</b>,
 <i class='BibTitle'>Analysis on Symmetric Cones</i>,
 <span class='BibPublisher'>Clarendon Press</span>
 (<span class='BibYear'>1994</span>).
</p>


<p><a id="biBfaraut_analysis_2000" name="biBfaraut_analysis_2000"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>FKK+00</span>]   <b class='BibAuthor'>Faraut, J., Kaneyuki, S., Koranyi, A., Lu, Q.-k. and Roos, G.</b>,
 <i class='BibTitle'>Analysis and Geometry on Complex Homogeneous
      Domains</i>,
 <span class='BibPublisher'>Birkhäuser</span>,
 <span class='BibSeries'>Progress in mathematics</span> (<span class='BibNumber'>185</span>),
 <span class='BibAddress'>Boston</span>
 (<span class='BibYear'>2000</span>).
</p>


<p><a id="biBhoggar_t-designs_1982" name="biBhoggar_t-designs_1982"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Hog82</span>]   <b class='BibAuthor'>Hoggar, S. G.</b>,
 <i class='BibTitle'>t-Designs in projective spaces</i>,
 <span class='BibJournal'>European Journal of Combinatorics</span>,
 <em class='BibVolume'>3</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>1982</span>),
 <span class='BibPages'>233--254</span>.
</p>


<p><a id="biBhoggar_t-designs_1992" name="biBhoggar_t-designs_1992"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Hog92</span>]   <b class='BibAuthor'>Hoggar, S. G.</b>,
<a href="http://www.sciencedirect.com/science/article/pii/S0195669805800320"><i class='BibTitle'>t-Designs with general angle set</i></a>,
 <span class='BibJournal'>European Journal of Combinatorics</span>,
 <em class='BibVolume'>13</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>1992</span>),
 <span class='BibPages'>257--271</span>.
</p>


<p><a id="biBlyubich_tight_2009" name="biBlyubich_tight_2009"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Lyu09</span>]   <b class='BibAuthor'>Lyubich, Y. I.</b>,
<a href="https://doi.org/10.1007/s10623-008-9240-4"><i class='BibTitle'>On tight projective designs</i></a>,
 <span class='BibJournal'>Designs, Codes and Cryptography</span>,
 <em class='BibVolume'>51</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2009</span>),
 <span class='BibPages'>21--31</span>.
</p>


<p><a id="biBmccrimmon_taste_2004" name="biBmccrimmon_taste_2004"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>McC04</span>]   <b class='BibAuthor'>McCrimmon, K.</b>,
<a href="https://www.springer.com/gp/book/9780387954479"><i class='BibTitle'>A Taste of Jordan Algebras</i></a>,
 <span class='BibPublisher'>Springer-Verlag</span>,
 <span class='BibSeries'>Universitext</span>,
 <span class='BibAddress'>New York</span>
 (<span class='BibYear'>2004</span>).
</p>


<p><a id="biBnasmith_octonions_2022" name="biBnasmith_octonions_2022"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Nas22</span>]   <b class='BibAuthor'>Nasmith, B.</b>,
<a href="https://alco.centre-mersenne.org/articles/10.5802/alco.215/"><i class='BibTitle'>Octonions and the two strictly projective tight 5-designs</i></a>,
 <span class='BibJournal'>Algebraic Combinatorics</span>,
 <em class='BibVolume'>5</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2022</span>),
 <span class='BibPages'>401--411</span>.
</p>


<p><a id="biBnasmith_tight_2023" name="biBnasmith_tight_2023"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Nas23</span>]   <b class='BibAuthor'>Nasmith, B.</b>,
<a href="https://espace.rmc.ca/jspui/handle/11264/1423"><i class='BibTitle'>Tight Projective 5-Designs and Exceptional
      Structures</i></a>,
 <span class='BibType'>{PhD} {Thesis}</span>,
 <span class='BibSchool'>Royal Military College of Canada</span>,
 <span class='BibAddress'>Kingston ON</span>
 (<span class='BibYear'>2023</span>)<br />
(<span class='BibNote'>Accepted: 2023-07-27T12:24:01Z</span>).
</p>


<p><a id="biBspringer_octonions_2000" name="biBspringer_octonions_2000"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>SV00</span>]   <b class='BibAuthor'>Springer, T. A. and Veldkamp, F. D.</b>,
<a href="https://www.springer.com/gp/book/9783540663379"><i class='BibTitle'>Octonions, Jordan Algebras and Exceptional
      Groups</i></a>,
 <span class='BibPublisher'>Springer-Verlag</span>,
 <span class='BibSeries'>Springer {Monographs} in {Mathematics}</span>,
 <span class='BibAddress'>Berlin Heidelberg</span>
 (<span class='BibYear'>2000</span>).
</p>


<p><a id="biBwilson_finite_2009" name="biBwilson_finite_2009"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Wil09a</span>]   <b class='BibAuthor'>Wilson, R. A.</b>,
<a href="https://www.springer.com/gp/book/9781848009875"><i class='BibTitle'>The Finite Simple Groups</i></a>,
 <span class='BibPublisher'>Springer-Verlag</span>,
 <span class='BibSeries'>Graduate {Texts} in {Mathematics}</span>,
 <span class='BibAddress'>London</span>
 (<span class='BibYear'>2009</span>).
</p>


<p><a id="biBwilson_octonions_2009" name="biBwilson_octonions_2009"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Wil09b</span>]   <b class='BibAuthor'>Wilson, R. A.</b>,
<a href="https://linkinghub.elsevier.com/retrieve/pii/S0021869309001458"><i class='BibTitle'>Octonions and the Leech lattice</i></a>,
 <span class='BibJournal'>Journal of Algebra</span>,
 <em class='BibVolume'>322</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2009</span>),
 <span class='BibPages'>2186--2190</span>.
</p>


<p><a id="biBwilson_conways_2011" name="biBwilson_conways_2011"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Wil11</span>]   <b class='BibAuthor'>Wilson, R. A.</b>,
<a href="https://www.degruyter.com/view/j/jgth.2011.14.issue-1/jgt.2010.038/jgt.2010.038.xml"><i class='BibTitle'>Conway's group and octonions</i></a>,
 <span class='BibJournal'>Journal of Group Theory</span>,
 <em class='BibVolume'>14</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2011</span>),
 <span class='BibPages'>1--8</span>.
</p>

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