Biorderability of knot quandles of knots up to eight crossings

The paper investigates biorderability of knot quandles of prime knots up to eight crossings. We prove that knot quandles of knots 6₃, 8₇, 8₈, 8₁₀ and 8₁₆ can not be biorderable. However, we see that knot quandles of knots 4₁, 6₁, 6₂, 7₆, 7₇, 8₁, 8₂, 8₃, 8₄, 8₅, 8₆, 8₉, 8₁₁, 8₁₂, 8₁₃, 8₁₄, 8₁₇, 8₁₈, 8₂₀ and 8₂₁ could be biorderable. We also give linear orders on the generating set of the knot quandle of a knot (among these knots) that could be extendable to biorders on the quandle.