Speaking of hypothetical structures, you can get, with little cheating, infinitely large “alkane” like poly(heptane-1,1-diyl)[1]
where $n=\infty$, i.e. with infinite degree of polymerization (or substituted branched ones like those in other, correct, answers, with even bigger infinity sizes).
Notes:
- Alternative structure-based polymer name based on older organic chemistry nomenclature would be poly(1-heptylidene). However the “longest chain” rule seems to applied differently in polymer nomenclature, so somewhat more “preferred name” could be poly(hexylmethylene).