TOKYO, Oct 26 (Reuters) - Japan’s Nikkei share average rallied strongly on Tuesday, fuelled by earnings optimism and following overnight Wall Street gains that took the Dow and S&P 500 to record highs. The Nikkei closed 1.8% higher at 29,106.01, after surging at the open and holding those gains through the afternoon. Heavy-weights including Uniqlo-owner Fast Retailing and SoftBank Group jumped 5% and 2.2%, respectively. The broader Topix advanced 1.2% to 2,018.40, with 31 of its 33 sectors posting gains, led by a 3% rally in shippers . At the other end, banks slipped 0.3% and airlines were little changed. “There was no particular catalyst beyond the U.S. stock highs,” said a market participant at a domestic securities firm. U.S. e-mini futures pointed to a 0.3% rise at the re-open for the S&P 500, and an index of Asia-Pacific stocks outside Japan also edged higher, further supporting sentiment. A large proportion of S&P 500 companies are due to report results this week, including technology heavyweights Apple, Amazon, Microsoft, and Google-operator Alphabet, which have been the drivers of the Wall Street rally this year. Sony Group rose 2.6% to its highest since 2000 ahead of earnings results on Thursday. “Before earnings season gets into full swing, the market is focused on the psychologically important 29,000 level (for the Nikkei), and investors may want to take a wait-and-see attitude there,” said another market participant at a domestic securities firm. Other noteable gainers were Panasonic, rallying 5.6% after unveiling a prototype battery to help key customer Tesla lower costs. Telecom company NTT gained 5.4% amid investor optimism over a revised medium-term business strategy revealed Monday. Toyota Group supplier Denso rose 2.9% following a target price upgrade at Nomura Securities. Toyota Motor added 1.7%. Reporting by Tokyo markets team; editing by Uttaresh.V and Rashmi Aich Our Standards: The Thomson Reuters Trust Principles.