If using arame or hijiki, place it in a medium bowl and cover with warm water.
Let it soak until very soft, about 30 minutes. If using instant wakame, follow package directions (usually 5-10 minutes).
Drain the rehydrated seaweed, making sure to reserve at least 2 tablespoons (30 ml / 1 fl oz) of the mineral-rich soaking liquid.
Combine the drained seaweed, your choice of oil, sake or rice wine vinegar, a sprinkle of salt, and 2 tablespoons (30 ml / 1 fl oz) of the reserved soaking water in a high-speed blender.
Blend on high for about 30-60 seconds, or until a thick, creamy emulsion forms. Stop the blender, scrape down the sides to incorporate any stray pieces of seaweed, and blend again for a few seconds until perfectly smooth.
Taste the mayonnaise and add more salt if needed.
Serve immediately or transfer to an airtight jar and store in the refrigerator.