Mishnah Berurah — משנה ברורה

Does not exempt - And [regarding] a טלית whose warp [threads] are from the same material [as the ציצית strings] and the weft/woof [threads] are from wool, or vice versa... he should affix wool ציצית specifically, for they [alone] exempt all other materials... and [he should] not [use ציצית strings] from other materials... even if the majority [of the garment] was from other materials... for the warp or weft/woof alone is not considered a garment, as was mentioned previously in Se'if Kattan 1. And even if you can't recognize the wool threads on their own... like if you mixed the wool threads a little bit into the [threads that are on the] warp and weft/woof , and you can't recognize their place, [meaning] where they are... even here it appears that it's better to make the ציצית from wool strings... because there are those who say that they (ie. the wool threads that were mixed in) are considered to be threads and are not nullified [to the rest of the non-wool garment]. And it's even better to make the entire garment out of wool without any admixture at all from other materials... and with that he will be adorned above. And a garment that is [made of] a mixture of cotton and linen... this garment has no way of fixing it, unless it's an extenuating circumstance [in which case] he should make for it ציצית strings of linen... as was mentioned previously at the end of Se'if Kattan 8.