The cheapest way to get around 20,000 miles on a Star Alliance Carrier would be to take United to the Far East/Australia/India. Look up United's Pacific E-Fares on their website www.ual.com (they change often). A couple of current examples listed below. Aside from that you can buy a consolidated ticket to Singapore on Lufthansa from Toronto for around CAD $1500 and go via Frankfurt. I'm been told that Cathay Pacific has some great fares out of Vancouver; however I have no personal experience in that regard since my home is in Toronto
Pacific Economy E-Fares
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Chicago (ORD)Auckland (AKL) $925.00
Los Angeles (LAX)Delhi (DEL) $900.00