On May 24 you can fly SQ in economy BKK-NRT for $38 USD one-way (.8095 cents USD per mile flown) and on July 25 for $61 one-way by booking through Airpaz (some OTA I have never used). Google will initially show the $38/$61 price if you search for a one-way flight, but it will re-price when you select the flight. The trick is to select a roundtrip flight NRT-BKK-NRT including the cheap SQ segment, then the final page will provide two links to OTA's - one for the outbound flight and another for the return, which is the cheap SQ flight.
$38 Flight -
https://www.google.com/travel/flight...hl=en&gl=en_US
$61 Flight -
https://www.google.com/travel/flight...hl=en&gl=en_US
Booking Links (Click on Continue, then choose the Airpaz option, ignore the other flight on the itinerary)
$38 Flight -
https://www.google.com/travel/flight...y7efqFjS1NhQj9
$61 Flight -
https://www.google.com/travel/flight...aV7ekzrwxUxZ77
Airpaz