According to the FINRA, the rules permit a pattern day trader to trade up to four times the maintenance margin excess in the account as of the close of business of the previous day. So if you have \$26,000 in your account you can only trade \$1,000? Or am I thinking about this wrong? And if this is the case, how do higher frequency trading strategies manage to work?
If you have \$26k, and no positions on, your maintenance excess is \$26k, so your day trading buying power, DTBP, is \$26k * 4 = \$104k in DTBP. You are confusing account minimum with maintenance excess, different concepts.
Having worked at a shop directly supporting HFTs, I can say in general that they have MUCH larger account sizes. One issue to consider if doing an HFT-type strategy is how does your broker handle open-order exposure.