spaces are obtainable by surgery on knots in the 3-sphere?

We first discuss this question for lens spaces of

type $(p,q)$ with small $p$ or $q$. Next, we will

particularly show that lens spaces containing Klein

bottles are unobtainable by Berge's surgery on doubly

primitive knots. We also give an algorithm to determine

whether a given lens space is obtainable by Berge's

surgery on doubly primitive knots.