There are a couple of ways
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There are a couple of ways to put HD on a DVD. None of them will play in a conventional DVD player.
Some very small number of regular DVD players have supported alternate formats, including HD, but this is very specific to your player. The more common formats here are DivX-HD and WMV/HD. DivX-HD is just a DivX file authored at standard bitrates specified by DivX, Inc. They work with hardware manufacturers to ensure compatibility. WMV/HD is a fully authored format, based on specs defined by Microsoft, using HTML and Javascript. There’s virtually no authoring software, though, so it’s a bit of hand coding. I had a player that played both of these types, before real HD standards emerged.
Aside from that, you need a Blu-ray player or PC to play HD video. Most Blu-ray players support the AVCHD format on DVD, which is a subset and slight mutation of Blu-ray. This was created by Sony and Panasonic for DVD camcorders, but you can put your HD videos on AVCHD disc and expect them to play in most BD players and many PCs. The main limitation is that you must use AVC, not MPEG-2 or VC-1, and the bitrate should be below 18Mb/s.