At one point, the court appears to assume this is the case. At page 67, the court says, "His sentence of death, although it cannot be implemented under current law, also remains valid." But law is more than statutes. Regulations and case law are also law. In any event, this statement is dictum, as the possibility of replacing electrocution with another method without legislation was not the issue before the court. The dispositive language is this, on pages 68-69 (footnotes omitted):

And Nebraska’s statutes specifying electrocution as the mode of inflicting the death penalty are separate, and severable, from the procedures by which the trial court sentences the defendant....

On direct appeal in a capital case, our responsibility extends beyond the validity of the conviction and sentence. We are also charged with the duty to administer and supervise the implementation of the death penalty by appointing the day for execution of the sentence and issuing a death warrant. It is in exercising that duty that we have considered whether electrocution is constitutional. And obviously, the State cannot carry out Mata’s sentence without a constitutionally acceptable method of execution.

Thus, although we affirm the judgment, we decline to “appoint a day certain for the execution of the sentence” and stay Mata’s execution. When the State moves that an execution date be set, in addition to the other requirements for such a motion, the State should allege, and be prepared to demonstrate, that a constitutionally acceptable method of carrying out Mata’s sentence is available.

Because the method-of-execution statute is invalid but severable, the state of the law in Nebraska is the same as if the Legislature had provided for the death penalty but not specified the manner of execution. Can the death penalty be constitutionally carried out in that situation? It certainly could in the nineteenth century. That was the issue actually before the Supreme Court in Wilkerson v. Utah, 99 U.S. 130 (1878). In the coverage of Baze v. Rees, that case has commonly been misreported as addressing a substantive Eighth Amendment challenge to the firing squad, but it did not. Here is the actual holding of the case:

Had the statute prescribed the mode of executing the sentence, it would have been the duty of the court to follow it, unless the punishment to be inflicted was cruel and unusual, within the meaning of the Eighth Amendment to the Constitution, which is not pretended by the counsel of the prisoner. Statutory directions being given that the prisoner when duly convicted shall suffer death, without any statutory regulation specifically pointing out the mode of executing the command of the law, it must be that the duty is devolved upon the court authorized to pass the sentence to determine the mode of execution and to impose the sentence prescribed. [Citation.]

Persons guilty of murder in the first degree "shall suffer death," are the words of the territorial statute, and when that provision is construed in connection with sec. 10 of the code previously referred to, it is clear that it is made obligatory upon the court to prescribe the mode of executing the sentence of death which the code imposes where the conviction is for murder in the first degree, subject, of course, to the constitutional prohibition, that cruel and unusual punishment shall not be inflicted.

So, if the Nebraska court follows Wilkerson, it is now the court's duty to prescribe the method of execution if the Legislature does not act. The executive branch should develop a method and submit it to the court for approval in connection with the motion to set a date mentioned in the Mata opinion.