A primitive symmetric association scheme of class d is naturally embedded as
a spherical s-distance set in the Euclidean space, where s is at most d. Bannai
and Bannai proved that Larman-Rogers-Seidel's ratio of the 2-distance set is
instantly read in the character table of the association scheme of class 2. In
2009, the second author generalized Larman-Rogers-Seidel's ratio to any
s-distance set.

By Seidel's switching, we construct new strongly regular graphs with
parameters $(276,140,58,84)$. In this paper, we simplify the known switching
theorem due to Bose and Shrikhande as follows.

Let $G=(V,E)$ be a primitive strongly regular graph with parameters
$(v,k,\lambda,\mu)$.

Let $S(G,H)$ be the graph from $G$ by switching with respect to a nonempty
$H\subset V$.

Suppose $v=2(k-\theta_1)$ where $\theta_1$ is the nontrivial positive
eigenvalue of the $(0,1)$ adjacency matrix of $G$. This strongly regular graph
is associated with a regular two-graph.

Let $X$ be a finite subset of Euclidean space $\mathbb{R}^d$. We define for
each $x \in X$, $B(x):=\{(x,y) \mid y \in X, x \ne y, (x,x) \geq (y,y)\}$ where
$(,)$ denotes the standard inner product. $X$ is called an inside $s$-inner
product set if $|B(x)| \leq s$ for all $x\in X$. In this paper, we prove that
the cardinalities of inside $s$-inner product sets have the Fisher type upper
bound. An inside $s$-inner product set is said to be tight if its cardinality
attains the Fisher type upper bound. Tight inside $s$-inner product sets are
closely related to tight Euclidean designs.