No, you can't open your own 401k. You can contribute to an IRA. The limit is 5500 for 2018. Note not all 401k have employer matches.
You will be eligible for a Pension Plan benefit (i.e. be vested) when you complete six years of service (if you were enrolled in the FRS prior to July 1, 2011) or eight years of service (if you were enrolled in the FRS on or after July 1, 2011).
Self-employed individuals should consider SEP IRAs, SIMPLE IRAs, solo 401(k)s, or solo Roth 401(k)s, with professional financial advice.
Open a SIMPLE IRA through a bank or another financial institution. Set up a SIMPLE IRA plan at any time January 1 through October 1. If you became self-employed after October 1, you can set up a SIMPLE IRA plan for the year as soon as administratively feasible after your business starts.
employed person can arrange to set up and contribute to a 401(k) plan. If there are employees, there are certain rules that may require the individual to offer the plan to them as well, though you may not need to contribute. If you have no employees you can set up a ``solo'' 401(k) plan, which you can research.
When you're self-employed, you can save for retirement with tax-advantaged accounts like a SEP IRA, self-employed 401(k), SIMPLE IRA, or Fidelity Advantage 401(k)℠. A health savings plan (HSA) is another potential option for long-term savings, particularly since savings are not use it or lose it and can grow over time.
You could use a traditional solo 401(k) or a Roth solo 401(k) for potential tax benefits. Once again, you receive the same tax benefits as you would with other self-employed retirement plans. A traditional solo 401(k) gives you an up-front tax deduction for contributions, but the withdrawals are taxed in retirement.