A sect, known as the Tzedukim, after one of its founders, Tzadok, believed in the absolutely literal interpretation of the Torah. Therefore, they said that when the Torah says "on the day after the Shabbat," it meant "Shabbat" in its regular meaning, the Seventh Day of the week, and therefore, according to this sadly mistaken view, the Count of the Omer would always begin on Sunday!
This is in direct opposition to the view accepted by Jewish tradition, that in this instance, the expression "mimachorat ha-Shabbat," "the day after Shabbat," means the day after the first day of Passover, since all of the holy days in Judaism carry the main aspect of Shabbbat; namely, the sanctification of time.
One of the proofs is that the Torah says that "chadash" may not be eaten until this very day (that the "Omer" is brought). And it says in Yehoshua (Chapter 5) that the Jewish People "ate from the (new) produce of the Land 'mimachorat ha-Pesach,' " the only time that the holiday is called Pesach (Passover) in all of the Bible." Here it is made absolutely clear that the day following the eating of the Passover sacrifice is the day on which the "Omer" is brought, the bringing of which is the "matir," the action which lifts a prohibition, as in our case, the prohibition against eating "chadash."
And in our time, since we don't bring the "Minchat HaOmer," the "Omer Grain Offering," it is the day itself; that is, the sixteenth of Nisan, when in Temple times, the Omer was brought, that is the "matir," that which lifts the prohibition.