er ▁wishes ▁to ▁share ▁a ▁secret ▁S , ▁only ▁the ▁rows ▁of ▁A ▁whose ▁last ▁entry ▁is ▁S ▁are ▁used ▁in ▁the ▁scheme . ▁The ▁deal er ▁randomly ▁selects ▁one ▁of ▁these ▁rows , ▁and ▁hands ▁out ▁to ▁player ▁i ▁the ▁entry ▁in ▁this ▁row ▁in ▁column ▁i ▁as ▁shares . ▁ ▁F actor ial ▁designs ▁ ▁A ▁factor ial ▁experiment ▁is ▁a ▁statist ically ▁struct ured ▁experiment ▁in ▁which ▁several ▁factors ▁( water ing ▁levels , ▁ant ib iot ics , ▁fert il izers , ▁etc .) ▁are ▁applied ▁to ▁each ▁experimental ▁unit ▁at ▁varying ▁( but ▁integral ) ▁levels ▁( high , ▁low , ▁or ▁various ▁intermediate ▁levels ). ▁In ▁a ▁full ▁factor ial ▁experiment ▁all ▁combinations ▁of ▁levels ▁of ▁the ▁factors ▁need ▁to ▁be ▁tested , ▁but ▁to ▁minim ize ▁conf ounding ▁influ ences ▁the ▁levels ▁should ▁be ▁varied ▁within ▁any ▁experimental ▁run . ▁ ▁An ▁orthogonal ▁array ▁of ▁strength ▁ 2 ▁can ▁be ▁used ▁to ▁design ▁a ▁factor ial ▁experiment . ▁The ▁columns ▁represent ▁the ▁various ▁factors ▁and ▁the ▁entries ▁are ▁the ▁levels ▁that ▁the ▁factors ▁can ▁be ▁applied ▁at ▁( ass uming ▁that ▁all ▁factors ▁can ▁be ▁applied ▁at ▁the ▁same ▁number ▁of ▁levels ). ▁An ▁experimental ▁run ▁is ▁a ▁row ▁of ▁the ▁orthogonal ▁array , ▁that ▁is , ▁apply ▁the ▁corresponding ▁factors ▁at ▁the ▁levels ▁which ▁appear ▁in ▁the ▁row . ▁When ▁using ▁one ▁of ▁these ▁designs , ▁the ▁treatment ▁units ▁and ▁trial ▁order ▁should ▁be ▁random ized ▁as ▁much ▁as ▁the ▁design ▁allows . ▁For ▁example