# Balanced and general $MAXkSAT$ known approximation results and bounds from $UGC$

$$MAX2SAT$$ has a $$0.9401$$ to $$0.9402$$ approximation algorithm which is conjectured to be optimal by $$UGC$$ while there is a balanced $$MAX2SAT$$ bound of $$0.943$$ approximation which is conjectured to be optimal by $$UGC$$.

1. For other values of $$k$$ do we know the optimal values conjectured by $$UGC$$ for both balanced and general situations and the status of algorithmically achievable results known?
1. A sanity check for $$MAXSAT$$: For $$MAXSAT$$ it is $$NP$$-hard to beat $$7/8$$ approximation and we have an algorithm which achieves $$7/8$$ and do we know $$UGC$$ provides the same bound for both balanced and general situations (I am unable to locate what $$UGC$$ says about $$MAXSAT$$ and we know if $$UGC$$ says a strictly lower than $$7/8$$ bound then trivially $$UGC$$ is false and so this sanity check)?