The Mishnah is discussing a Karpaf that was not enclosed for the purpose of living within its walls ("Lo Hukaf l'Dirah"). Earlier in the Mishnah, Rebbi Yehudah ben Bava teaches that if a Karpaf which is Beis Se'asayim in size does not have a Beis Dirah in it, one may not carry within its walls. Tosfos (DH u'Bilvad) writes that according to Rebbi Yehudah ben Bava, the same would apply to a Karpaf that is smaller than Beis Se'asayim -- presumably even if it is one by two Amos. It would seem, then, that the same applies according to Rebbi Eliezer. If its length is more than twice its width and it is not Hukaf l'Dirah, it should be a Karmelis and not a Reshus ha'Yachid no matter how small it is.

However, Tosfos later (25b DH Karpaf) seems to be in doubt about this point. His first answer seems to accept what we wrote above, but in his second answer he writes that if the Karpaf is "Mashehu" -- any amount -- smaller than Beis Se'asayim, it is a Reshus ha'Yachid even though its length is more than twice its width.

Your question has Halachic ramifications as well. The opinion of Rebbi Eliezer is cited l'Halachah (OC 358:1). The PRI MEGADIM, REBBI AKIVA EIGER, and later the MISHNAH BERURAH there quote the Tosfos who writes that if the Karpaf is smaller than Beis Se'asayim, it is a Reshus ha'Yachid even though its length is more than twice its width. The CHAZON ISH (25:11) argues that the other Rishonim disagree with the second answer of Tosfos, and therefore his second answer should not be accepted l'Halachah. (The MAHARSHAM in Da'as Torah brings a TOSEFTA cited by the MILCHAMOS here that seems to argue with Tosfos' suggestion as well.)

In addition, I have problems with Tosfos' second answer. How can more than Beis Se'asayim (always Karmelis), exactly Beis Se'asayim (Karmelis if its length is not greater than its width), and less than Beis Se'asayim (always Reshus ha'Yachid) have three different Halachos? Tosfos himself (23a DH u'Bilvad) writes that it is not acceptable to suggest that sizes within three "Mashehu's" have three different Halachos! (I later noticed that the Chazon Ish, ibid., raises this question on Tosfos and leaves it unanswered.)

I would therefore suggest that Tosfos's intention is that depending on how much less than Beis Se'asayim the Karpaf is, that is how much more the length may be than double the width. (The word "Mashehu" in Tosfos should read "Mah she'Hu", two words.) But I did not see this understanding of Tosfos in the Poskim.

I hope this helps you,

Mordecai Kornfeld