Best Known (226−57, 226, s)-Nets in Base 3
(226−57, 226, 324)-Net over F3 — Constructive and digital
Digital (169, 226, 324)-net over F3, using
- 31 times duplication [i] based on digital (168, 225, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 75, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- trace code for nets [i] based on digital (18, 75, 108)-net over F27, using
(226−57, 226, 908)-Net over F3 — Digital
Digital (169, 226, 908)-net over F3, using
(226−57, 226, 38519)-Net in Base 3 — Upper bound on s
There is no (169, 226, 38520)-net in base 3, because
- 1 times m-reduction [i] would yield (169, 225, 38520)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 225211 492828 644640 070462 602671 327980 485583 910597 097259 825793 963397 581077 172160 652646 316132 568722 424934 457793 > 3225 [i]