$t$-adic symmetric multiple zeta values for indices in which 1 and 3 appear alternately

This paper deals with the $t$-adic symmetric multiple zeta values modulo $t^m$ without modulo $\pi^2$ reduction for indices in which $1$ and $3$ appear alternately. We investigate those values that can be expressed as a polynomial of the Riemann zeta values, and give a conjecturally complete list of explicit formulas for such values.