Best Known (171, 171+54, s)-Nets in Base 3
(171, 171+54, 464)-Net over F3 — Constructive and digital
Digital (171, 225, 464)-net over F3, using
- 31 times duplication [i] based on digital (170, 224, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 56, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 56, 116)-net over F81, using
(171, 171+54, 1103)-Net over F3 — Digital
Digital (171, 225, 1103)-net over F3, using
(171, 171+54, 51661)-Net in Base 3 — Upper bound on s
There is no (171, 225, 51662)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 225144 784136 221267 646993 622796 524720 571647 859309 030093 264833 581872 554973 542860 576899 498269 755704 271747 515345 > 3225 [i]