BENGALURU, Dec 1 (Reuters) - Indian shares edged higher on Tuesday following their best monthly gain since April, with sentiment lifted by a smaller-than-expected contraction in Asia’s third-largest economy and broader optimism stemming from hopes for a COVID-19 vaccine. The NSE Nifty 50 index rose 0.15% to 12,988 by 0350 GMT, while the benchmark S&P BSE Sensex was up 0.11% at 44,198.47, after closing out November with gains of more than 11% each. Indian stock markets were closed on Monday for a holiday. Government data released after market hours on Friday showed Asia’s third-largest economy contracted by 7.5% in the September quarter, versus an 8.8% contraction expected in a Reuters poll, amid signs of a pick-up in manufacturing. Investors are now awaiting monthly auto sales data due later in the day. The Nifty Auto Index was flat in early trading. (Reporting by Chris Thomas in Bengaluru; Editing by Subhranshu Sahu)