Part of speech tagging

I have been working on language processing algorithms and used an online PoS tagger for the following sentence:
"Let us meet same day next week"
The results was -
"Let|VB us|PRP meet|VB same|JJ day|NN next|IN week|NN"

I noticed that while the word 'same' is determined to be an adjective, the word 'next' is tagged as a preposition.
Is this correct in this context, considering that the word 'same' has same semantic relation to 'day' as the word 'next' has to 'week'?