I'm looking for a rug or a floor covering made out of a substance called
"plinyl". It's kind of like vinyl floor covering only it's a bit more
mat-like-- and it comes in large rug-like sheets. Can't seem to locate
the word anywhere via a google search. I saw a plinyl rug in a
specialty home furnishing store in East Hampton. THe store owners said
the material came from a Scandinavian country (I think).

I am confident that the floor covering you're looking for is "Plynyl,"
which is made by Chilewich.

"Plynyl is an innovative soft surfaced flooring invented for the
designer looking to provide their clients with alternatives to
traditional flooring. Available in rolls, tiles and pre-cut mats,
Plynyl provides rich woven textures and colors for the floor ranging
from high-tech 'metallics' to the natural look of sisals.

Plynyl is woven vinyl fabric bonded to a soft polyurethane cushion."

Plynyl.com
http://www.plynyl.com/plynyl.html

Here you'll find a contact form to request information about Plynyl:

Chilewich.com
http://chilewich.com/plynyl/contact.html

You might be interested in the attractive Chilewich mats and rugs on these sites:

Unica Home
http://www.unicahome.com/catalog/index.asp?cid=1937

Room and Company
http://www.roomandcompany.com/collections/chilewich/floormat_rolls.shtml

Velocity Art and Design
http://www.velocityartanddesign.com/chilewich.html

Sadelier
http://www.sadelier.com/custom_furnishings/rugs/Chilewich/

Pique4U
http://www.pique4u.com/Productpage8.htm

Google search strategy:

Google Web Search: "plynyl"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=plynyl

Google Web Search: "chilewich" + "vinyl"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=chilewich+vinyl

I hope this is helpful. If I've misidentified the flooring material
that you seek, or if a link doesn't work for you, please request
clarification; I'll gladly offer further assistance before you rate my
answer.

Best regards,
pinkfreud