Nevada Revised Statute (NRS) section 129.080 states that “Any minor who is at least 16 years of age, who is married or living apart from his or her parents or legal guardian, and who is a resident of the county, may petition the juvenile court of that county for a decree of emancipation.”

So, in order to petition the court for emancipation, you must be at least age 16 and either be married or already be living apart from your parents. This is reinforced by NRS § 129.090(1), which states that in a court petition for emancipation, the minor must set forth the following:
(a) The name, age and address of the minor;
(b) The names and addresses of the parents of the minor;
(c) The name and address of any legal guardian of the minor;
(d) If no parent or guardian can be found, the name and address of the child’s nearest known relative residing within this state;
(e) Facts relating to the minor’s education, employment, and length of residence apart from his or her parents or guardian;
(f) That the minor willingly lives apart from his or her parents or legal guardian with the consent or acquiescence of his or her parents or legal guardian;
(g) That the minor is managing his or her own financial affairs;

(h) That the source of the minor’s income is not derived from any activity declared to be a crime by the laws of this state or the United States; and
(i) That the minor is attending school or has been excused from attending school pursuant to NRS 392.040 to 392.125, inclusive.

(Bolding added.) Note in particular (f) & (g), which I bolded. You need to be able to state in your petition that you are already living apart from your parents with their consent and that you are already managing your own financial affairs. The two statutes taken together reinforce that you need to be already living independently of your parents without financial support from someone else in order to succeed in petitioning the court for emancipation. You do not meet that requirement, and that coupled by opposition by your parents to the emancipation, I think will mean a court will not approve your petition for emancipation. It certainly would not be easy, and if you really wanted to succeed, you’d likely need a lawyer to do it. I suggest if you are set on this that you consult a family law attorney in Nevada to find out if you have any shot at all here and what it would cost you try. Your desire for what you perceive to be a shot at a better education in another state is commendable, as far as that goes, but by itself isn’t enough to win emancipation.