A major promise of the incoming administration is to improve our infrastructure. The problem with this, of course, is knowing how to pay for it without increasing the federal debt. This has been done successfully in the past using US Notes, starting with President Lincoln and so the relevant legislation in place today needs to be understood. Extensive material is available online at the link below  .
One of the criticisms leveled against this type of funding is that our double-entry accounting system was not in place 150 years ago, and therefore this type of funding is not possible today. This short essay shows that this is not a valid criticism.
For point of clarity, the money we normally see in circulation are Federal Reserve Notes and are issued by the private banking system at interest and against debt, but notes of public monies are issued by the Treasury at no interest and without debt.
Seigniorage is an important part of this analysis, and is simply the difference between the cost of producing money and the value received by the government upon its issuance. For instance, if it costs 1 cent to print a dollar bill, then the seigniorage from issuing it to the public would be 99 cents. The cost of producing electronic money, which accounts for about 97% of all monies in circulation, is essentially zero, meaning that the seigniorage on it is about 100%. Further, considering that there are trillions of US dollars in circulation, both in the US and internationally (for trade, central bank reserves, and even criminal activities) seigniorage, although not regularly discussed, is a huge issue.
Currently the federal government only collects seigniorage on the coins which the Mint, a division of the Treasury, produces. Collectively the coins are worth more than their cost of production and therefore bring in seigniorage. The coins are bought with an account entry into the Treasury account (at the Fed) for the face value of the coins. For historical reasons, dollar bills do not accrue seigniorage to the Treasury. They are printed by the Bureau of Engraving and Printing (BEP), also a division of Treasury, but instead they are bought by the Federal Reserve System for the cost of production. The thinking behind this came from the gold standard era in that the Fed held the gold legally needed for backing and the BEP was solely a service organization for the Fed working at cost. When the US went off the gold standard internally in 1933 this arrangement was never changed.
The Federal Accounting Standards Advisory Board (FASAB) is clear on how seigniorage is to be handled as a source of income. In the latest edition of the FASAB Handbook of Federal Accounting Standards and Other Pronouncements as Amended as of June 30, 2016 it states:
"Other financing sources from the public
305. Seigniorage.--Seigniorage is the face value of newly minted coins less the cost of production (which includes the cost of the metal, manufacturing, and transportation). It results from the sovereign power of the Government to directly create money and, although not an inflow of resources from the public, does increase the Government's net position in the same manner as an inflow of resources. Because it is not demanded, earned, or donated, it is another financing source rather than revenue. It should be recognized as an other financing source when coins are delivered to the Federal Reserve Banks in return for deposits."  [highlight by author]
"Net position" is explained later. As seen above, the official technical term for the account item category within which seigniorage fits is "other financing source"
This language is repeated almost verbatim in the annual report of the Mint, except it adds:
"Therefore, the President's budget excludes seigniorage from receipts and treats it as a means of financing."
Seigniorage, therefore, is well understood under government accounting as a source of income not involving "a transfer of assets from the public" (see above quote). The issuance of public money therefore by Treasury to fund infrastructure improvements would procure 100% of the seigniorage to Treasury resulting in lower taxes, and/or better services, and/or lower deficits and accumulated debt.
In the Congressional Research Service bulletin The Debt Limit: History and Recent Increases  it states that US Notes are not part of current debt limitation legislation. The same is reflected in the Treasury's regular Monthly Statement of the Public Debt (MSPD)  . Therefore public monies, as these are issued by the Treasury and not the Fed, are uncommon or "other" debt as they incur no future obligation. One could call them "no-debt debt".
Government accounting does not show "equity" in its balance sheets, but instead it does show "net position". Net position is government accounting-speak for equity on the balance sheet; i.e., the increase in monetary assets can be balanced by an increase in equity, instead of debt liabilities. This is mandated in the FASAB Handbook on page 39 of SFFAC 2  . In the quote in the Seigniorage Section 2 above from the FASAB, it states clearly: "Seigniorage " does increase the government's net position [read that as equity] in the same manner as an inflow of resources." This means that the current manner of treating the creation of Treasury coins as an increase in net position (equity) would apply to the creation of public money by the Treasury as well. No accounting methodological change is needed. The face value of this newly created money, as done today with coins, is then credited to the Treasury's account at the Fed.
Public/sovereign money could be likened to costless-to-produce "digital gold" (or silver, or oil, or any other asset/resource), and that might help us see how the accounting for public/sovereign money works and makes sense, i.e., when oil is struck, its value net of costs is booked as an asset, with no corresponding liability on the balance sheet, so it is a net asset, and thus increases the assets on one side of the balance sheet and the equity (or net position) on the other side, and the balance sheet is balanced that way. This is analogous, as public/sovereign money is not debt.