Before revision:  We develop a new class of "curtain" sketchesthat are a bit more complex than Martingale LogLog but with substantially better } , e. g., Martingale Curtain has MVP \approx 2.31. We also prove that Martingale Fishmonger has   an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
After revision:  We develop a new class of "curtain" sketchesthat are a bit more complex than Martingale LogLog but with substantially better } of 10. Our contributions are as follows. Cohen and Ting independently discovered what we call the Martingale transform for converting a mergeable sketch into a non-mergeable sketch. We present a simpler way to analyze the limiting MVP of Martingale-type sketches. We prove that the an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.