In this paper we show that if
X is an
s-distance set in
$
{\left| X \right|} \leqslant {\sum\nolimits_{i = 0}^{2p - 1} {{\left( {{*{20}c}
{{m + s - i - 1}} \\
{{s - i}} \\
} \right)}} }
$
{\left| X \right|} \leqslant {\sum\nolimits_{i = 0}^{2p - 1} {{\left( {\begin{array}{*{20}c}
{{m + s - i - 1}} \\
{{s - i}} \\
\end{array} } \right)}} }
Moreover if
X is antipodal, then
$
{\left| X \right|} \leqslant 2{\sum\nolimits_{i = 0}^{p - 1} {{\left( {{*{20}c}
{{m + s - 2i - 2}} \\
{{m - 1}} \\
} \right)}} }
$
{\left| X \right|} \leqslant 2{\sum\nolimits_{i = 0}^{p - 1} {{\left( {\begin{array}{*{20}c}
{{m + s - 2i - 2}} \\
{{m - 1}} \\
\end{array} } \right)}} }
.
Mathematics Subject
Classification (2000): 05E99 - 05B99 - 51M99 - 62K99